Theorem an12s 565

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 561 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 561	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ph /\ ( ps /\ ch ) ) )
2		an12s.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylbi 121	1 |- ( ( ps /\ ( ph /\ ch ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  anabsan2  584  1stconst  6330  2ndconst  6331  sbthlemi5  7089  iccshftr  10151  iccshftl  10153  iccdil  10155  icccntr  10157  zfz1iso  11023  ndvdsadd  12357  neipsm  14741