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Theorem bnj1436 34853
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 2885 . 2 (𝑥𝐴𝜑)
32biimpi 216 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  wcel 2108  {cab 2714
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816
This theorem is referenced by:  bnj1517  34864  bnj66  34874  bnj900  34943  bnj1296  35035  bnj1371  35043  bnj1374  35045  bnj1398  35048  bnj1450  35064  bnj1497  35074  bnj1498  35075  bnj1514  35077  bnj1501  35081
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