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Theorem bnj1538 30179
 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}
21rabeq2i 3170 . 2 (𝑥𝐴 ↔ (𝑥𝐵𝜑))
32simprbi 479 1 (𝑥𝐴𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∈ wcel 1977  {crab 2900 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-tru 1478  df-ex 1696  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-rab 2905 This theorem is referenced by:  bnj1279  30340  bnj1311  30346  bnj1418  30362  bnj1312  30380  bnj1523  30393
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