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Theorem bnj937 33126
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 1728 . 2  |-  ( E. x ps  <->  ps )
31, 2sylib 196 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  bnj1265  33167  bnj1379  33185  bnj852  33275  bnj1148  33348  bnj1154  33351  bnj1189  33361  bnj1245  33366  bnj1286  33371  bnj1311  33376  bnj1371  33381  bnj1374  33383  bnj1498  33413  bnj1514  33415
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