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Theorem bj-abbi2i 33637
 Description: Remove dependency on ax-13 2342 from abbi2i 2920. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-abbi2i.1 (𝑥𝐴𝜑)
Assertion
Ref Expression
bj-abbi2i 𝐴 = {𝑥𝜑}
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bj-abbi2i
StepHypRef Expression
1 bj-abeq2 33634 . 2 (𝐴 = {𝑥𝜑} ↔ ∀𝑥(𝑥𝐴𝜑))
2 bj-abbi2i.1 . 2 (𝑥𝐴𝜑)
31, 2mpgbir 1779 1 𝐴 = {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 207   = wceq 1520   ∈ wcel 2079  {cab 2773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789  ax-5 1886  ax-6 1945  ax-7 1990  ax-8 2081  ax-9 2089  ax-10 2110  ax-11 2124  ax-12 2139  ax-ext 2767 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1523  df-ex 1760  df-nf 1764  df-sb 2041  df-clab 2774  df-cleq 2786  df-clel 2861 This theorem is referenced by:  bj-abid2  33642  bj-termab  33702  bj-df-nul  33892
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