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Theorem bnj1538 34702
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 = {𝑥𝐵𝜑}
Assertion
Ref Expression
bnj1538 (𝑥𝐴𝜑)

Proof of Theorem bnj1538
StepHypRef Expression
1 bnj1538.1 . . 3 𝐴 = {𝑥𝐵𝜑}
21reqabi 3442 . 2 (𝑥𝐴 ↔ (𝑥𝐵𝜑))
32simprbi 495 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1534  wcel 2099  {crab 3419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-12 2167  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-rab 3420
This theorem is referenced by:  bnj1279  34865  bnj1311  34871  bnj1418  34887  bnj1312  34905  bnj1523  34918
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