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Theorem bnj1436 31427
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 2912 . 2 (𝑥𝐴𝜑)
32biimpi 208 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1653  wcel 2157  {cab 2785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-12 2213  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-tru 1657  df-ex 1876  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795
This theorem is referenced by:  bnj1517  31437  bnj66  31447  bnj900  31516  bnj1296  31606  bnj1371  31614  bnj1374  31616  bnj1398  31619  bnj1450  31635  bnj1497  31645  bnj1498  31646  bnj1514  31648  bnj1501  31652
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