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Theorem bnj1247 32104
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1247.1  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
Assertion
Ref Expression
bnj1247  |-  ( ph  ->  th )

Proof of Theorem bnj1247
StepHypRef Expression
1 bnj1247.1 . 2  |-  ( ph  <->  ( ps  /\  ch  /\  th 
/\  ta ) )
2 id 22 . 2  |-  ( th 
->  th )
31, 2bnj771 32059 1  |-  ( ph  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ w-bnj17 31976
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 31977
This theorem is referenced by:  bnj1110  32275  bnj1128  32283  bnj1245  32307
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