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Theorem bnj1538 30686
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 3187 . 2 (𝑥𝐴 ↔ (𝑥𝐵𝜑))
32simprbi 480 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1480  wcel 1987  {crab 2912
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-12 2044  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1483  df-ex 1702  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-rab 2917
This theorem is referenced by:  bnj1279  30847  bnj1311  30853  bnj1418  30869  bnj1312  30887  bnj1523  30900
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