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Theorem rabeqi 2605
Description: Equality theorem for restricted class abstractions. Inference form of rabeq 2604. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
rabeqi.1  |-  A  =  B
Assertion
Ref Expression
rabeqi  |-  { x  e.  A  |  ph }  =  { x  e.  B  |  ph }
Distinct variable groups:    x, A    x, B
Allowed substitution hint:    ph( x)

Proof of Theorem rabeqi
StepHypRef Expression
1 nfcv 2223 . 2  |-  F/_ x A
2 nfcv 2223 . 2  |-  F/_ x B
3 rabeqi.1 . 2  |-  A  =  B
41, 2, 3rabeqif 2603 1  |-  { x  e.  A  |  ph }  =  { x  e.  B  |  ph }
Colors of variables: wff set class
Syntax hints:    = wceq 1285   {crab 2357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rab 2362
This theorem is referenced by:  phimullem  10981
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