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Theorem bnj1219 29270
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1219.1  |-  ( ch  <->  (
ph  /\  ps  /\  ze ) )
bnj1219.2  |-  ( th  <->  ( ch  /\  ta  /\  et ) )
Assertion
Ref Expression
bnj1219  |-  ( th 
->  ps )

Proof of Theorem bnj1219
StepHypRef Expression
1 bnj1219.2 . 2  |-  ( th  <->  ( ch  /\  ta  /\  et ) )
2 bnj1219.1 . . 3  |-  ( ch  <->  (
ph  /\  ps  /\  ze ) )
32simp2bi 974 . 2  |-  ( ch 
->  ps )
41, 3bnj835 29226 1  |-  ( th 
->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ w3a 937
This theorem is referenced by:  bnj1379  29300
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 179  df-an 362  df-3an 939
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