Theorem an42 518

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 517	. 2 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (ps /\ th)))
2		ancom 446	. . 3 |- ((ps /\ th) <-> (th /\ ps))
3	2	anbi2i 491	. 2 |- (((ph /\ ch) /\ (ps /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))
4	1, 3	bitri 180	1 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))

Syntax hints:   <-> wb 153   /\ wa 230

This theorem is referenced by:  an42s 520  pssn2lp 2198  brecop2 4368  aceq1 4791  prlem934b 5203  prlem934 5204  divmul13 5840  divmul24 5841

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 154  df-an 232

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