Theorem an42 582

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 581	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ th ) ) )
2		ancom 264	. . 3 |- ( ( ps /\ th ) <-> ( th /\ ps ) )
3	2	anbi2i 454	. 2 |- ( ( ( ph /\ ch ) /\ ( ps /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )
4	1, 3	bitri 183	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ ch ) /\ ( th /\ ps ) ) )

Syntax hints:   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  rnlem  971  supmoti  6970  distrnqg  7349  distrnq0  7421  prcdnql  7446  prcunqu  7447