Theorem bimsc1 904

Description: Removal of conjunct from one side of an equivalence. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem bimsc1

Step	Hyp	Ref	Expression
1		simpr 447	. . . 4 |- ((ps /\ ph) -> ph)
2		ancr 532	. . . 4 |- ((ph -> ps) -> (ph -> (ps /\ ph)))
3	1, 2	impbid2 195	. . 3 |- ((ph -> ps) -> ((ps /\ ph) <-> ph))
4	3	bibi2d 309	. 2 |- ((ph -> ps) -> ((ch <-> (ps /\ ph)) <-> (ch <-> ph)))
5	4	biimpa 470	1 |- (((ph -> ps) /\ (ch <-> (ps /\ ph))) -> (ch <-> ph))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)