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Theorem bnj1517 29198
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 29188 . 2  |-  ( x  e.  A  ->  ( ph  /\  ps ) )
32simprd 449 1  |-  ( x  e.  A  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1632    e. wcel 1696   {cab 2282
This theorem is referenced by:  bnj1286  29365  bnj1450  29396  bnj1501  29413
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292
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