Theorem 3ancomb 1017

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 1016	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )
2		3anrot 1014	. 2 |- ( ( ps /\ ph /\ ch ) <-> ( ph /\ ch /\ ps ) )
3	1, 2	bitri 184	1 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )

This proof depends on syntax axioms:   <-> wb 105   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  3simpb  1026  addcanprg  7983  elioore  10314  swrdswrd  11477  pcgcd  13108  ablsubsub23  14129  xmetrtri  15477