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Theorem bnj1538 28932
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1538.1  |-  A  =  { x  e.  B  |  ph }
Assertion
Ref Expression
bnj1538  |-  ( x  e.  A  ->  ph )

Proof of Theorem bnj1538
StepHypRef Expression
1 bnj1538.1 . . 3  |-  A  =  { x  e.  B  |  ph }
21rabeq2i 2913 . 2  |-  ( x  e.  A  <->  ( x  e.  B  /\  ph )
)
32simprbi 451 1  |-  ( x  e.  A  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    e. wcel 1721   {crab 2670
This theorem is referenced by:  bnj1279  29093  bnj1311  29099  bnj1418  29115  bnj1312  29133  bnj1523  29146
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 1662  ax-8 1683  ax-11 1757  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-rab 2675
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