Theorem 3ancoma 892

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

Assertion

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

Proof of Theorem 3ancoma

Step	Hyp	Ref	Expression
1		ancom 253	. . 3 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	anbi1i 431	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ps /\ ph ) /\ ch ) )
3		df-3an 887	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
4		df-3an 887	. 2 |- ( ( ps /\ ph /\ ch ) <-> ( ( ps /\ ph ) /\ ch ) )
5	2, 3, 4	3bitr4i 201	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )

Syntax hints:   /\ wa 97   <-> 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:  3ancomb  893  3anrev  895  3anan12  897  3com12  1108  elfzmlbp  8990  elfzo2  9007