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Theorem bnj1254 32158
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1254.1  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
Assertion
Ref Expression
bnj1254  |-  ( ph  ->  ta )

Proof of Theorem bnj1254
StepHypRef Expression
1 bnj1254.1 . 2  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
2 id 22 . . 3  |-  ( ta 
->  ta )
32bnj708 32103 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ta )  ->  ta )
41, 3sylbi 195 1  |-  ( ph  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ w-bnj17 32029
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-bnj17 32030
This theorem is referenced by:  bnj554  32247  bnj557  32249  bnj967  32293  bnj999  32305  bnj907  32313  bnj1118  32330  bnj1128  32336  bnj1253  32363  bnj1450  32396
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