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Theorem bnj1232 29567
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 29510 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ta )  ->  ps )
31, 2sylbi 198 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ w-bnj17 29443
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  df-3an 984  df-bnj17 29444
This theorem is referenced by:  bnj605  29670  bnj607  29679  bnj944  29701  bnj969  29709  bnj970  29710  bnj1001  29721  bnj1110  29743  bnj1118  29745  bnj1128  29751  bnj1145  29754  bnj1311  29785
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