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Theorem opelresg 4962
 Description: Ordered pair membership in a restriction. Exercise 13 of [TakeutiZaring] p. 25. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
opelresg

Proof of Theorem opelresg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opeq2 3797 . . 3
21eleq1d 2349 . 2
31eleq1d 2349 . . 3
43anbi1d 685 . 2
5 vex 2791 . . 3
65opelres 4960 . 2
72, 4, 6vtoclbg 2844 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1623   wcel 1684  cop 3643   cres 4691 This theorem is referenced by:  brresg  4963  opelresiOLD  4966  opelresi  4967  issref  5056 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-res 4701
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