Theorem 3anrot 780

Description: Rotation law for triple conjunction.

Assertion

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

Proof of Theorem 3anrot

Step	Hyp	Ref	Expression
1		ancom 435	. 2 |- ((ph /\ (ps /\ ch)) <-> ((ps /\ ch) /\ ph))
2		3anass 779	. 2 |- ((ph /\ ps /\ ch) <-> (ph /\ (ps /\ ch)))
3		df-3an 777	. 2 |- ((ps /\ ch /\ ph) <-> ((ps /\ ch) /\ ph))
4	1, 2, 3	3bitr4 183	1 |- ((ph /\ ps /\ ch) <-> (ps /\ ch /\ ph))

Syntax hints:   <-> wb 146   /\ wa 223   /\ w3a 775

This theorem is referenced by:  3ancomb 783  3anrev 784  3simpc 787  fr3nr 2926  wefrc 2943  ordelord 2970  brinxp2 3231  omword 4201  oeword 4217  nnleltp1t 5954  mulc1cncf 7279  ipassr 8506

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 777

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