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Theorem bnj1436 32010
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 2945 . 2 (𝑥𝐴𝜑)
32biimpi 217 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  wcel 2105  {cab 2796
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1531  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890
This theorem is referenced by:  bnj1517  32021  bnj66  32031  bnj900  32100  bnj1296  32190  bnj1371  32198  bnj1374  32200  bnj1398  32203  bnj1450  32219  bnj1497  32229  bnj1498  32230  bnj1514  32232  bnj1501  32236
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