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Theorem bnj1517 31046
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 31036 . 2 (𝑥𝐴 → (𝜑𝜓))
32simprd 478 1 (𝑥𝐴𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383   = wceq 1523  wcel 2030  {cab 2637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-12 2087  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1526  df-ex 1745  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647
This theorem is referenced by:  bnj1286  31213  bnj1450  31244  bnj1501  31261
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