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Theorem rabeqf 3080
 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 2602 . . 3
4 eleq2 2502 . . . 4
54anbi1d 709 . . 3
63, 5abbid 2564 . 2
7 df-rab 2791 . 2
8 df-rab 2791 . 2
96, 7, 83eqtr4g 2495 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1870  cab 2414  wnfc 2577  crab 2786 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791 This theorem is referenced by:  rabeq  3081  fpwrelmapffs  28162  rabeq12f  32104
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