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Theorem bnj534 29596
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj534.1  |-  ( ch 
->  ( E. x ph  /\ 
ps ) )
Assertion
Ref Expression
bnj534  |-  ( ch 
->  E. x ( ph  /\ 
ps ) )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x)    ch( x)

Proof of Theorem bnj534
StepHypRef Expression
1 bnj534.1 . 2  |-  ( ch 
->  ( E. x ph  /\ 
ps ) )
2 19.41v 1840 . 2  |-  ( E. x ( ph  /\  ps )  <->  ( E. x ph  /\  ps ) )
31, 2sylibr 217 1  |-  ( ch 
->  E. x ( ph  /\ 
ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 375   E.wex 1673
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674
This theorem is referenced by:  bnj600  29778  bnj852  29780
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