Theorem 3anrot 939

Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994.)

Assertion

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

Proof of Theorem 3anrot

Step	Hyp	Ref	Expression
1		ancom 437	. 2 |- ((ph /\ (ps /\ ch)) <-> ((ps /\ ch) /\ ph))
2		3anass 938	. 2 |- ((ph /\ ps /\ ch) <-> (ph /\ (ps /\ ch)))
3		df-3an 936	. 2 |- ((ps /\ ch /\ ph) <-> ((ps /\ ch) /\ ph))
4	1, 2, 3	3bitr4i 268	1 |- ((ph /\ ps /\ ch) <-> (ps /\ ch /\ ph))

Syntax hints:   <-> wb 176   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  3ancomb  943  3anrev  945  3simpc  954  oqelins4  5795  leaddc2  6216  lemuc2  6255