Theorem an12s 571

Description: Swap two conjuncts in antecedent. The label suffix "s" means that an12 567 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 567	. 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 )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  anabsan2  590  1stconst  6457  2ndconst  6458  sbthlemi5  7278  iccshftr  10396  iccshftl  10398  iccdil  10400  icccntr  10402  zfz1iso  11293  ndvdsadd  12698  neipsm  15255