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Theorem bnj1266 29281
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1266.1  |-  ( ch 
->  E. x ( ph  /\ 
ps ) )
Assertion
Ref Expression
bnj1266  |-  ( ch 
->  E. x ps )

Proof of Theorem bnj1266
StepHypRef Expression
1 bnj1266.1 . 2  |-  ( ch 
->  E. x ( ph  /\ 
ps ) )
2 simpr 449 . 2  |-  ( (
ph  /\  ps )  ->  ps )
31, 2bnj593 29211 1  |-  ( ch 
->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   E.wex 1551
This theorem is referenced by:  bnj1265  29282
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
  Copyright terms: Public domain W3C validator