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Theorem bnj1538 31460
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 3410 . 2 (𝑥𝐴 ↔ (𝑥𝐵𝜑))
32simprbi 492 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1656  wcel 2164  {crab 3121
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-12 2220  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1660  df-ex 1879  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-rab 3126
This theorem is referenced by:  bnj1279  31621  bnj1311  31627  bnj1418  31643  bnj1312  31661  bnj1523  31674
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