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Theorem bj-abbidv 31967
Description: Remove dependency on ax-13 2234 from abbidv 2728. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-abbidv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
bj-abbidv (𝜑 → {𝑥𝜓} = {𝑥𝜒})
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem bj-abbidv
StepHypRef Expression
1 nfv 1830 . 2 𝑥𝜑
2 bj-abbidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2bj-abbid 31966 1 (𝜑 → {𝑥𝜓} = {𝑥𝜒})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195   = wceq 1475  {cab 2596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603
This theorem is referenced by:  bj-cdeqab  31975
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