Theorem bimsc1 823

Description: Removal of conjunct from one side of an equivalence.

Assertion

Ref	Expression
bimsc1	|- (((ph -> ps) /\ (ch <-> (ps /\ ph))) -> (ch <-> ph))

Proof of Theorem bimsc1

Step	Hyp	Ref	Expression
1		id 73	. 2 |- ((ch <-> (ps /\ ph)) -> (ch <-> (ps /\ ph)))
2		pm4.71r 698	. . . 4 |- ((ph -> ps) <-> (ph <-> (ps /\ ph)))
3	2	biimpi 168	. . 3 |- ((ph -> ps) -> (ph <-> (ps /\ ph)))
4	3	bicomd 580	. 2 |- ((ph -> ps) -> ((ps /\ ph) <-> ph))
5	1, 4	sylan9bbr 600	1 |- (((ph -> ps) /\ (ch <-> (ps /\ ph))) -> (ch <-> ph))

Syntax hints:   -> wi 3   <-> wb 163   /\ wa 240

This theorem is referenced by:  bm1.3ii 3441

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

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