Theorem 3ancoma 891

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 886	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
4		df-3an 886	. 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 884

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 886

This theorem is referenced by:  3ancomb  892  3anrev  894  3anan12  896  3com12  1107  elfzmlbp  8760  elfzo2  8777