Theorem 3ancoma 926

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 262	. . 3 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2	1	anbi1i 445	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ps /\ ph ) /\ ch ) )
3		df-3an 921	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
4		df-3an 921	. 2 |- ( ( ps /\ ph /\ ch ) <-> ( ( ps /\ ph ) /\ ch ) )
5	2, 3, 4	3bitr4i 210	1 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )

Syntax hints:   /\ wa 102   <-> wb 103   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  3ancomb  927  3anrev  929  3anan12  931  3com12  1142  elfzmlbp  9143  elfzo2  9160