Theorem an32 526

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 393	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		an12 525	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ps /\ ( ph /\ ch ) ) )
3		ancom 262	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ( ph /\ ch ) /\ ps ) )
4	1, 2, 3	3bitri 204	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Syntax hints:   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  an32s  532  3anan32  930  indifdir  3220  inrab2  3237  reupick  3248  unidif0  3941  resco  4845  f11o  5179  respreima  5316  dff1o6  5436  dfoprab2  5572  xpassen  6327  enq0enq  6621  elioomnf  8991