Theorem an42 554

Description: Rearrangement of 4 conjuncts. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
an42	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )

Proof of Theorem an42

Step	Hyp	Ref	Expression
1		an4 553	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )
2		ancom 262	. . 3 |- ( ( ps /\ th ) <-> ( th /\ ps ) )
3	2	anbi2i 445	. 2 |- ( ( ( ph /\ ch ) /\ ( ps /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )
4	1, 3	bitri 182	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ 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:  rnlem  922  supmoti  6688  distrnqg  6946  distrnq0  7018  prcdnql  7043  prcunqu  7044