Theorem an42 389

Description: Rearrangement of 4 conjuncts.

Assertion

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

Proof of Theorem an42

Step	Hyp	Ref	Expression
1		an4 388	. 2 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (ps /\ th)))
2		ancom 333	. . 3 |- ((ps /\ th) <-> (th /\ ps))
3	2	anbi2i 367	. 2 |- (((ph /\ ch) /\ (ps /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))
4	1, 3	bitr 151	1 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))

Syntax hints:   <-> wb 127   /\ wa 196

This theorem is referenced by:  an42s 391  pssn2lp 1571  brecop2 3243  aceq1 3552  prlem934b 3932  prlem934 3933

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org