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Theorem bianir 975
Description: If a wff is equivalent to its conjunction with another wff, the other wwf follows. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Roger Witte, 17-Aug-2020.)
Assertion
Ref Expression
bianir  |-  ( (
ph  /\  ( ps  <->  ph ) )  ->  ps )

Proof of Theorem bianir
StepHypRef Expression
1 biimpr 201 . 2  |-  ( ( ps  <->  ph )  ->  ( ph  ->  ps ) )
21impcom 431 1  |-  ( (
ph  /\  ( ps  <->  ph ) )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ wa 370
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 188  df-an 372
This theorem is referenced by:  suppimacnv  6936  bnj970  29766  bnj1001  29777  bj-bibibi  31174
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