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Theorem bnj1517 31252
 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 31242 . 2 (𝑥𝐴 → (𝜑𝜓))
32simprd 477 1 (𝑥𝐴𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382   = wceq 1630   ∈ wcel 2144  {cab 2756 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-12 2202  ax-ext 2750 This theorem depends on definitions:  df-bi 197  df-an 383  df-tru 1633  df-ex 1852  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766 This theorem is referenced by:  bnj1286  31419  bnj1450  31450  bnj1501  31467
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