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Theorem bnj1436 34601
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}
21eqabri 2869 . 2 (𝑥𝐴𝜑)
32biimpi 215 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wcel 2098  {cab 2702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-12 2166  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802
This theorem is referenced by:  bnj1517  34612  bnj66  34622  bnj900  34691  bnj1296  34783  bnj1371  34791  bnj1374  34793  bnj1398  34796  bnj1450  34812  bnj1497  34822  bnj1498  34823  bnj1514  34825  bnj1501  34829
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