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Theorem bnj1517 28560
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 28550 . 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 1649    e. wcel 1717   {cab 2374
This theorem is referenced by:  bnj1286  28727  bnj1450  28758  bnj1501  28775
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384
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