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Theorem bnj926 29115
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj926  |-  ( (
ph  /\  ( ps  <->  ph ) )  ->  ps )

Proof of Theorem bnj926
StepHypRef Expression
1 bicom 191 . 2  |-  ( ( ps  <->  ph )  <->  ( ph  <->  ps ) )
2 bi1 178 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
32impcom 419 . 2  |-  ( (
ph  /\  ( ph  <->  ps ) )  ->  ps )
41, 3sylan2b 461 1  |-  ( (
ph  /\  ( ps  <->  ph ) )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  bnj970  29295  bnj1001  29306
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
  Copyright terms: Public domain W3C validator