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Theorem bnj1232 28836
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 28777 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ta )  ->  ps )
31, 2sylbi 187 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w-bnj17 28711
This theorem is referenced by:  bnj605  28939  bnj607  28948  bnj944  28970  bnj969  28978  bnj970  28979  bnj1001  28990  bnj1110  29012  bnj1118  29014  bnj1128  29020  bnj1145  29023  bnj1311  29054
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 28712
  Copyright terms: Public domain W3C validator