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Theorem bnj1538 29300
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 2955 . 2  |-  ( x  e.  A  <->  ( x  e.  B  /\  ph )
)
32simprbi 452 1  |-  ( x  e.  A  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653    e. wcel 1726   {crab 2711
This theorem is referenced by:  bnj1279  29461  bnj1311  29467  bnj1418  29483  bnj1312  29501  bnj1523  29514
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-rab 2716
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