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Theorem opelresg 4619
 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 3550 . . 3
21eleq1d 2106 . 2
31eleq1d 2106 . . 3
43anbi1d 438 . 2
5 vex 2560 . . 3
65opelres 4617 . 2
72, 4, 6vtoclbg 2614 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243   wcel 1393  cop 3378   cres 4347 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819  df-xp 4351  df-res 4357 This theorem is referenced by:  brresg  4620  opelresi  4623  issref  4707
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