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Theorem bnj534 29084
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 1854 . 2  |-  ( E. x ( ph  /\  ps )  <->  ( E. x ph  /\  ps ) )
31, 2sylibr 203 1  |-  ( ch 
->  E. x ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wex 1531
This theorem is referenced by:  bnj600  29267  bnj852  29269
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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