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Theorem rabeqi 38332
 Description: Equality theorem for restricted class abstractions. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
rabeqi.1 𝐴 = 𝐵
Assertion
Ref Expression
rabeqi {𝑥𝐴𝜑} = {𝑥𝐵𝜑}
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem rabeqi
StepHypRef Expression
1 nfcv 2751 . 2 𝑥𝐴
2 nfcv 2751 . 2 𝑥𝐵
3 rabeqi.1 . 2 𝐴 = 𝐵
41, 2, 3rabeqif 38320 1 {𝑥𝐴𝜑} = {𝑥𝐵𝜑}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  {crab 2900 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-13 2234  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  df-clel 2606  df-nfc 2740  df-rab 2905 This theorem is referenced by:  smflimlem4  39660
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