Theorem 3anrot 778

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 777	. 2 |- ((ph /\ ps /\ ch) <-> (ph /\ (ps /\ ch)))
3		df-3an 775	. 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 773

This theorem is referenced by:  3ancomb 781  3anrev 782  3simpc 785  fr3nr 2916  wefrc 2933  ordelord 2960  brinxp2 3221  omword 4185  oeword 4201  nnleltp1t 5901  mulc1cncf 7214  ipassr 8437

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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