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Theorem rabeqf 2951
 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 2581 . . 3
4 eleq2 2499 . . . 4
54anbi1d 687 . . 3
63, 5abbid 2551 . 2
7 df-rab 2716 . 2
8 df-rab 2716 . 2
96, 7, 83eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  cab 2424  wnfc 2561  crab 2711 This theorem is referenced by:  rabeq  2952 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716
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