Theorem bj-consensusALT 32563

Description: Alternate proof of bj-consensus 32562. (Contributed by BJ, 30-Sep-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
bj-consensusALT	|- ( (if- ( ph , ps , ch ) \/ ( ps /\ ch ) ) <-> if- ( ph , ps , ch ) )

Proof of Theorem bj-consensusALT

Step	Hyp	Ref	Expression
1		orcom 402	. 2 |- ( (if- ( ph , ps , ch ) \/ ( ps /\ ch ) ) <-> ( ( ps /\ ch ) \/ if- ( ph , ps , ch ) ) )
2		anifp 1020	. . 3 |- ( ( ps /\ ch ) -> if- ( ph , ps , ch ) )
3		pm4.72 920	. . 3 |- ( ( ( ps /\ ch ) -> if- ( ph , ps , ch ) ) <-> (if- ( ph , ps , ch ) <-> ( ( ps /\ ch ) \/ if- ( ph , ps , ch ) ) ) )
4	2, 3	mpbi 220	. 2 |- (if- ( ph , ps , ch ) <-> ( ( ps /\ ch ) \/ if- ( ph , ps , ch ) ) )
5	1, 4	bitr4i 267	1 |- ( (if- ( ph , ps , ch ) \/ ( ps /\ ch ) ) <-> if- ( ph , ps , ch ) )

Syntax hints:   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384  if-wif 1012

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 197  df-or 385  df-an 386  df-ifp 1013

This theorem is referenced by: (None)