Theorem an42 587

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 586	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )
2		ancom 266	. . 3 |- ( ( ps /\ th ) <-> ( th /\ ps ) )
3	2	anbi2i 457	. 2 |- ( ( ( ph /\ ch ) /\ ( ps /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )
4	1, 3	bitri 184	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ 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:  rnlem  976  supmoti  6985  distrnqg  7364  distrnq0  7436  prcdnql  7461  prcunqu  7462