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Theorem bnj1232 32130
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 32073 . 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 32007
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 371  df-3an 967  df-bnj17 32008
This theorem is referenced by:  bnj605  32233  bnj607  32242  bnj944  32264  bnj969  32272  bnj970  32273  bnj1001  32284  bnj1110  32306  bnj1118  32308  bnj1128  32314  bnj1145  32317  bnj1311  32348
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