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Theorem bnj1232 34282
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 34225 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ta )  ->  ps )
31, 2sylbi 195 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ w-bnj17 34158
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 185  df-an 369  df-3an 973  df-bnj17 34159
This theorem is referenced by:  bnj605  34385  bnj607  34394  bnj944  34416  bnj969  34424  bnj970  34425  bnj1001  34436  bnj1110  34458  bnj1118  34460  bnj1128  34466  bnj1145  34469  bnj1311  34500
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