Theorem 3ancomb 893

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

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

Proof of Theorem 3ancomb

Step	Hyp	Ref	Expression
1		3ancoma 892	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )
2		3anrot 890	. 2 |- ( ( ps /\ ph /\ ch ) <-> ( ph /\ ch /\ ps ) )
3	1, 2	bitri 173	1 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )

Syntax hints:   <-> wb 98   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3simpb  902  addcanprg  6714  elioore  8781