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Theorem bnj1517 29490
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 29480 . 2  |-  ( x  e.  A  ->  ( ph  /\  ps ) )
32simprd 464 1  |-  ( x  e.  A  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370    = wceq 1437    e. wcel 1867   {cab 2405
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-12 1904  ax-ext 2398
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415
This theorem is referenced by:  bnj1286  29657  bnj1450  29688  bnj1501  29705
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