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Theorem bianir 968
Description: If a wff is equivalent to its conjunction with another wff, the other wwf follows. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Assertion
Ref Expression
bianir  |-  ( (
ph  /\  ( ps  <->  ph ) )  ->  ps )

Proof of Theorem bianir
StepHypRef Expression
1 bicom 200 . 2  |-  ( ( ps  <->  ph )  <->  ( ph  <->  ps ) )
2 bi1 186 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
32impcom 428 . 2  |-  ( (
ph  /\  ( ph  <->  ps ) )  ->  ps )
41, 3sylan2b 473 1  |-  ( (
ph  /\  ( ps  <->  ph ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 367
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 185  df-an 369
This theorem is referenced by:  suppimacnv  6912  bnj970  29319  bnj1001  29330  bj-bibibi  30726
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