Theorem an32 562

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 401	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		an12 561	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ps /\ ( ph /\ ch ) ) )
3		ancom 266	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ( ph /\ ch ) /\ ps ) )
4	1, 2, 3	3bitri 206	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105

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:  an32s  568  3anan32  1013  indifdir  3460  inrab2  3477  reupick  3488  unidif0  4251  resco  5233  f11o  5605  respreima  5763  dff1o6  5900  dfoprab2  6051  xpassen  6989  enq0enq  7618  elioomnf  10164  modfsummod  11969  pcqcl  12829  tx1cn  14943  isms2  15128  elcncf1di  15253