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Theorem bnj1142 29234
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1142.1  |-  ( ph  ->  A. x ( x  e.  A  ->  ps ) )
Assertion
Ref Expression
bnj1142  |-  ( ph  ->  A. x  e.  A  ps )

Proof of Theorem bnj1142
StepHypRef Expression
1 bnj1142.1 . 2  |-  ( ph  ->  A. x ( x  e.  A  ->  ps ) )
2 df-ral 2712 . 2  |-  ( A. x  e.  A  ps  <->  A. x ( x  e.  A  ->  ps )
)
31, 2sylibr 205 1  |-  ( ph  ->  A. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550    e. wcel 1726   A.wral 2707
This theorem is referenced by:  bnj1476  29292  bnj1533  29297  bnj1523  29514
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-ral 2712
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