Theorem an32 496

Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)

Assertion

Ref	Expression
an32	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Proof of Theorem an32

Step	Hyp	Ref	Expression
1		anass 381	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		an12 495	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ps /\ ( ph /\ ch ) ) )
3		ancom 253	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ( ph /\ ch ) /\ ps ) )
4	1, 2, 3	3bitri 195	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Syntax hints:   /\ wa 97   <-> wb 98

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:  an32s  502  3anan32  896  indifdir  3193  inrab2  3210  reupick  3221  unidif0  3920  resco  4825  f11o  5159  respreima  5295  dff1o6  5416  dfoprab2  5552  xpassen  6304  enq0enq  6529  elioomnf  8837