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Theorem bnj1211 29231
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1211.1  |-  ( ph  ->  A. x  e.  A  ps )
Assertion
Ref Expression
bnj1211  |-  ( ph  ->  A. x ( x  e.  A  ->  ps ) )

Proof of Theorem bnj1211
StepHypRef Expression
1 bnj1211.1 . 2  |-  ( ph  ->  A. x  e.  A  ps )
2 df-ral 2712 . 2  |-  ( A. x  e.  A  ps  <->  A. x ( x  e.  A  ->  ps )
)
31, 2sylib 190 1  |-  ( ph  ->  A. x ( 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:  bnj1533  29285  bnj1204  29443  bnj1523  29502
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-ral 2712
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