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Theorem rabeqf 2544
 Description: Equality theorem for restricted class abstractions, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 7-Mar-2004.)
Hypotheses
Ref Expression
rabeqf.1
rabeqf.2
Assertion
Ref Expression
rabeqf

Proof of Theorem rabeqf
StepHypRef Expression
1 rabeqf.1 . . . 4
2 rabeqf.2 . . . 4
31, 2nfeq 2182 . . 3
4 eleq2 2098 . . . 4
54anbi1d 438 . . 3
63, 5abbid 2151 . 2
7 df-rab 2309 . 2
8 df-rab 2309 . 2
96, 7, 83eqtr4g 2094 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1242   wcel 1390  cab 2023  wnfc 2162  crab 2304 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309 This theorem is referenced by:  rabeq  2545
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