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Theorem bnj1235 29153
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 19 . 2  |-  ( ch 
->  ch )
31, 2bnj770 29109 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w-bnj17 29027
This theorem is referenced by:  bnj966  29292  bnj967  29293  bnj910  29296  bnj1006  29307  bnj1018  29310  bnj1110  29328  bnj1121  29331  bnj1311  29370
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  df-3an 936  df-bnj17 29028
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