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Theorem bnj1517 32838
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1517.1 𝐴 = {𝑥 ∣ (𝜑𝜓)}
Assertion
Ref Expression
bnj1517 (𝑥𝐴𝜓)

Proof of Theorem bnj1517
StepHypRef Expression
1 bnj1517.1 . . 3 𝐴 = {𝑥 ∣ (𝜑𝜓)}
21bnj1436 32827 . 2 (𝑥𝐴 → (𝜑𝜓))
32simprd 496 1 (𝑥𝐴𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396   = wceq 1539  wcel 2106  {cab 2715
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-12 2171  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816
This theorem is referenced by:  bnj1286  33007  bnj1450  33038  bnj1501  33055
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