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Theorem bnj1517 29158
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1517.1  |-  A  =  { x  |  (
ph  /\  ps ) }
Assertion
Ref Expression
bnj1517  |-  ( x  e.  A  ->  ps )

Proof of Theorem bnj1517
StepHypRef Expression
1 bnj1517.1 . . 3  |-  A  =  { x  |  (
ph  /\  ps ) }
21bnj1436 29148 . 2  |-  ( x  e.  A  ->  ( ph  /\  ps ) )
32simprd 450 1  |-  ( x  e.  A  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    = wceq 1652    e. wcel 1725   {cab 2421
This theorem is referenced by:  bnj1286  29325  bnj1450  29356  bnj1501  29373
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431
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