An invalid contingency argument on SEP

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Bruce Reichenbach wrote the SEP article on cosmological arguments.  SEP articles are, I believe, peer-reviewed, and so we shouldn't expect them to contain invalid arguments.  This one does, however.  Here it is:

(1) A contingent being (a being such that if it exists, it could have not-existed or could cease to exist) exists.

(2) This contingent being has a cause of or explanation for its existence.

(3) The cause of or explanation for its existence is something other than the contingent being itself.

(4) What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.

(5) Contingent beings alone cannot provide a completely adequate causal account or explanation for the existence of a contingent being.

(6) Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.

(7) Therefore, a necessary being (a being such that if it exists, it cannot not-exist) exists.

(8) The universe is contingent.

(9) Therefore, the necessary being is something other than the universe.

What makes this argument invalid is pretty easy to see:  In step (5), there is talk of a "completely adequate" account or explanation, but never in previous steps.  So it can't be used to infer (6) as intended.  This can be easily fixed by changing step (2), but I'm still alarmed by the fact that a peer-reviewed article on SEP is invalid.

There are a couple of other anomalies which also trouble me.  For instance, step (3) is actually superfluous to the argument.  And step (4) is pretty close to being superfluous too, not required so long as (5) is suitably adjusted.  Finally, steps (1) and (8) could be combined for brevity.

The resulting argument would go something like this:

(10)  The universe exists and is a contingent being.  [Replaces (1) and (8).]

(11)  Its existence has a completely adequate explanation or causal account.  [Replaces (2).]

(12)  An explanation or causal account of the existence of a contingent being, such that all the existing beings involved are likewise contingent, isn't completely adequate.  [Replaces (5).]

(13)  Therefore, a necessary being, which is not itself the universe, exists, and is involved in a completely adequate explanation or causal account of the universe's existence.  [Replaces (6), (7), and (9).]

The above argument has the virtues of being shorter, clearer, and---most importantly---valid.

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