Theorem an12s 560

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 556 is combined with syl 14 (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 556	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ph /\ ( ps /\ ch ) ) )
2		an12s.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylbi 120	1 |- ( ( ps /\ ( ph /\ ch ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  anabsan2  579  1stconst  6200  2ndconst  6201  sbthlemi5  6938  iccshftr  9951  iccshftl  9953  iccdil  9955  icccntr  9957  zfz1iso  10776  ndvdsadd  11890  neipsm  12948