Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  rabeqf Unicode version

Theorem rabeqf 2676
 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 2289 . . 3
4 eleq2 2203 . . . 4
54anbi1d 460 . . 3
63, 5abbid 2256 . 2
7 df-rab 2425 . 2
8 df-rab 2425 . 2
96, 7, 83eqtr4g 2197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331   wcel 1480  cab 2125  wnfc 2268  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:  rabeqif  2677  rabeq  2678
 Copyright terms: Public domain W3C validator