Theorem 3ancoma 941

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 437	. . 3 |- ((ph /\ ps) <-> (ps /\ ph))
2	1	anbi1i 676	. 2 |- (((ph /\ ps) /\ ch) <-> ((ps /\ ph) /\ ch))
3		df-3an 936	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
4		df-3an 936	. 2 |- ((ps /\ ph /\ ch) <-> ((ps /\ ph) /\ ch))
5	2, 3, 4	3bitr4i 268	1 |- ((ph /\ ps /\ ch) <-> (ps /\ ph /\ ch))

Syntax hints:   <-> wb 176   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  3ancomb  943  3anrev  945  3anan12  947  3com12  1155  cnvsi  5519  oqelins4  5795  brpprod  5840