Theorem an32s 502

Description: Swap two conjuncts in antecedent. (Contributed by NM, 13-Mar-1996.)

Hypothesis

Ref	Expression
an32s.1	|- (((ph /\ ps) /\ ch) -> th)

Assertion

Ref	Expression
an32s	|- (((ph /\ ch) /\ ps) -> th)

Proof of Theorem an32s

Step	Hyp	Ref	Expression
1		an32 496	. 2 |- (((ph /\ ch) /\ ps) <-> ((ph /\ ps) /\ ch))
2		an32s.1	. 2 |- (((ph /\ ps) /\ ch) -> th)
3	1, 2	sylbi 114	1 |- (((ph /\ ch) /\ ps) -> th)

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  anass1rs  505  anabss1  510  fssres  5009  foco  5059  fun11iun  5090  fconstfvm  5322  isocnv  5394  f1oiso  5408  f1ocnvfv3  5444  genpassl  6507  genpassu  6508  cnegexlem3  6985  recexaplem2  7415  divap0  7445  qreccl  8351  xrlttr  8486