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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
StepHypRef Expression
1 simpr 447 . . . 4  |-  ( ( ps  /\  ph )  ->  ph )
2 ancr 532 . . . 4  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps 
/\  ph ) ) )
31, 2impbid2 195 . . 3  |-  ( (
ph  ->  ps )  -> 
( ( ps  /\  ph )  <->  ph ) )
43bibi2d 309 . 2  |-  ( (
ph  ->  ps )  -> 
( ( ch  <->  ( ps  /\ 
ph ) )  <->  ( ch  <->  ph ) ) )
54biimpa 470 1  |-  ( ( ( ph  ->  ps )  /\  ( ch  <->  ( ps  /\ 
ph ) ) )  ->  ( ch  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  bm1.3ii  4160
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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