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Theorem bnj1436 31138
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 2837 . 2 (𝑥𝐴𝜑)
32biimpi 206 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1596  wcel 2103  {cab 2710
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-12 2160  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1599  df-ex 1818  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720
This theorem is referenced by:  bnj1517  31148  bnj66  31158  bnj900  31227  bnj1296  31317  bnj1371  31325  bnj1374  31327  bnj1398  31330  bnj1450  31346  bnj1497  31356  bnj1498  31357  bnj1514  31359  bnj1501  31363
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