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Theorem bj-abbii 32412
Description: Remove dependency on ax-13 2250 from abbii 2742. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-abbii.1 (𝜑𝜓)
Assertion
Ref Expression
bj-abbii {𝑥𝜑} = {𝑥𝜓}

Proof of Theorem bj-abbii
StepHypRef Expression
1 bj-abbi 32410 . 2 (∀𝑥(𝜑𝜓) ↔ {𝑥𝜑} = {𝑥𝜓})
2 bj-abbii.1 . 2 (𝜑𝜓)
31, 2mpgbi 1722 1 {𝑥𝜑} = {𝑥𝜓}
Colors of variables: wff setvar class
Syntax hints:  wb 196   = wceq 1480  {cab 2612
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-ext 2606
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619
This theorem is referenced by:  bj-rababwv  32506
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