Theorem an42 798

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 797	. 2 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (ps /\ th)))
2		ancom 437	. . 3 |- ((ps /\ th) <-> (th /\ ps))
3	2	anbi2i 675	. 2 |- (((ph /\ ch) /\ (ps /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))
4	1, 3	bitri 240	1 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))

Syntax hints:   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  rnlem  931  fnpprod  5844