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Theorem bnj1538 32135
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 3466 . 2 (𝑥𝐴 ↔ (𝑥𝐵𝜑))
32simprbi 499 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  wcel 2114  {crab 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-12 2177  ax-ext 2792
This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1540  df-ex 1781  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-rab 3134
This theorem is referenced by:  bnj1279  32298  bnj1311  32304  bnj1418  32320  bnj1312  32338  bnj1523  32351
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