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Theorem bnj1436 32099
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 2946 . 2 (𝑥𝐴𝜑)
32biimpi 218 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1530  wcel 2107  {cab 2797
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 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-12 2169  ax-ext 2791
This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1533  df-ex 1774  df-sb 2063  df-clab 2798  df-cleq 2812  df-clel 2891
This theorem is referenced by:  bnj1517  32110  bnj66  32120  bnj900  32189  bnj1296  32281  bnj1371  32289  bnj1374  32291  bnj1398  32294  bnj1450  32310  bnj1497  32320  bnj1498  32321  bnj1514  32323  bnj1501  32327
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