Theorem an42 507

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 506	. 2 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (ps /\ th)))
2		ancom 435	. . 3 |- ((ps /\ th) <-> (th /\ ps))
3	2	anbi2i 480	. 2 |- (((ph /\ ch) /\ (ps /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))
4	1, 3	bitr 173	1 |- (((ph /\ ps) /\ (ch /\ th)) <-> ((ph /\ ch) /\ (th /\ ps)))

Syntax hints:   <-> wb 146   /\ wa 223

This theorem is referenced by:  an42s 509  pssn2lp 2147  brecop2 4307  aceq1 4729  prlem934b 5138  prlem934 5139  divmul13t 5782  divmul24t 5783

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 147  df-an 225

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