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Theorem bnj1517 33204
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 33194 . 2  |-  ( x  e.  A  ->  ( ph  /\  ps ) )
32simprd 463 1  |-  ( x  e.  A  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    = wceq 1379    e. wcel 1767   {cab 2452
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  ax-7 1739  ax-12 1803  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462
This theorem is referenced by:  bnj1286  33371  bnj1450  33402  bnj1501  33419
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