Theorem an12s 776

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 772 is combined with syl 15 (or a variant). (Contributed by NM, 13-Mar-1996.)

Hypothesis

Ref	Expression
an12s.1	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
an12s	|- ((ps /\ (ph /\ ch)) -> th)

Proof of Theorem an12s

Step	Hyp	Ref	Expression
1		an12 772	. 2 |- ((ps /\ (ph /\ ch)) <-> (ph /\ (ps /\ ch)))
2		an12s.1	. 2 |- ((ph /\ (ps /\ ch)) -> th)
3	1, 2	sylbi 187	1 |- ((ps /\ (ph /\ ch)) -> th)

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  anabsan2  795