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Theorem bnj937 29371
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj937.1  |-  ( ph  ->  E. x ps )
Assertion
Ref Expression
bnj937  |-  ( ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem bnj937
StepHypRef Expression
1 bnj937.1 . 2  |-  ( ph  ->  E. x ps )
2 19.9v 1804 . 2  |-  ( E. x ps  <->  ps )
31, 2sylib 199 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1659
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  bnj1265  29412  bnj1379  29430  bnj852  29520  bnj1148  29593  bnj1154  29596  bnj1189  29606  bnj1245  29611  bnj1286  29616  bnj1311  29621  bnj1371  29626  bnj1374  29628  bnj1498  29658  bnj1514  29660
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