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Theorem bnj1235 29176
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1235.1  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
Assertion
Ref Expression
bnj1235  |-  ( ph  ->  ch )

Proof of Theorem bnj1235
StepHypRef Expression
1 bnj1235.1 . 2  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
2 id 20 . 2  |-  ( ch 
->  ch )
31, 2bnj770 29132 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ w-bnj17 29050
This theorem is referenced by:  bnj966  29315  bnj967  29316  bnj910  29319  bnj1006  29330  bnj1018  29333  bnj1110  29351  bnj1121  29354  bnj1311  29393
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 178  df-an 361  df-3an 938  df-bnj17 29051
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