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Theorem rabeqi 2679
Description: Equality theorem for restricted class abstractions. Inference form of rabeq 2678. (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 2281 . 2 𝑥𝐴
2 nfcv 2281 . 2 𝑥𝐵
3 rabeqi.1 . 2 𝐴 = 𝐵
41, 2, 3rabeqif 2677 1 {𝑥𝐴𝜑} = {𝑥𝐵𝜑}
Colors of variables: wff set class
Syntax hints:   = wceq 1331  {crab 2420
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rab 2425
This theorem is referenced by:  phimullem  11907
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