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Theorem bnj1232 29248
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1232.1  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
Assertion
Ref Expression
bnj1232  |-  ( ph  ->  ps )

Proof of Theorem bnj1232
StepHypRef Expression
1 bnj1232.1 . 2  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
2 bnj642 29189 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ta )  ->  ps )
31, 2sylbi 189 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ w-bnj17 29123
This theorem is referenced by:  bnj605  29351  bnj607  29360  bnj944  29382  bnj969  29390  bnj970  29391  bnj1001  29402  bnj1110  29424  bnj1118  29426  bnj1128  29432  bnj1145  29435  bnj1311  29466
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 179  df-an 362  df-3an 939  df-bnj17 29124
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