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Theorem bj-abbi2i 32751
 Description: Remove dependency on ax-13 2244 from abbi2i 2736. (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 32748 . 2 (𝐴 = {𝑥𝜑} ↔ ∀𝑥(𝑥𝐴𝜑))
2 bj-abbi2i.1 . 2 (𝑥𝐴𝜑)
31, 2mpgbir 1724 1 𝐴 = {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   = wceq 1481   ∈ wcel 1988  {cab 2606 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-ext 2600 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616 This theorem is referenced by:  bj-abid2  32757  bj-termab  32821  bj-df-nul  32992
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