Theorem 3ancoma 780

Description: Commutation law for triple conjunction.

Assertion

Ref	Expression
3ancoma	|- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))

Proof of Theorem 3ancoma

Step	Hyp	Ref	Expression
1		ancom 435	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	anbi1i 480	. 2 |- (((ph /\ ps) /\ ch) <-> ((ps /\ ph) /\ ch))
3		df-3an 775	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
4		df-3an 775	. 2 |- ((ps /\ ph /\ ch) <-> ((ps /\ ph) /\ ch))
5	2, 3, 4	3bitr4 183	1 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))

Syntax hints:   <-> wb 146   /\ wa 223   /\ w3a 773

This theorem is referenced by:  3ancomb 781  3anrev 782  fncnv 3547  climcmplem 7073  efcn 7363  ablmuldiv 8044  nvadd12 8182  nvscom 8190  pilem1 8590  cnvadj 9733  hmeogrp 10425

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  df-3an 775

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