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Theorem bnj1436 30884
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1436.1 𝐴 = {𝑥𝜑}
Assertion
Ref Expression
bnj1436 (𝑥𝐴𝜑)

Proof of Theorem bnj1436
StepHypRef Expression
1 bnj1436.1 . . 3 𝐴 = {𝑥𝜑}
21abeq2i 2733 . 2 (𝑥𝐴𝜑)
32biimpi 206 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1481  wcel 1988  {cab 2606
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-12 2045  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1484  df-ex 1703  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616
This theorem is referenced by:  bnj1517  30894  bnj66  30904  bnj900  30973  bnj1296  31063  bnj1371  31071  bnj1374  31073  bnj1398  31076  bnj1450  31092  bnj1497  31102  bnj1498  31103  bnj1514  31105  bnj1501  31109
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