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Theorem resopab 5189
 Description: Restriction of a class abstraction of ordered pairs. (Contributed by NM, 5-Nov-2002.)
Assertion
Ref Expression
resopab
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem resopab
StepHypRef Expression
1 df-res 4892 . 2
2 df-xp 4886 . . . . . 6
3 vex 2961 . . . . . . . 8
43biantru 493 . . . . . . 7
54opabbii 4274 . . . . . 6
62, 5eqtr4i 2461 . . . . 5
76ineq2i 3541 . . . 4
8 incom 3535 . . . 4
97, 8eqtri 2458 . . 3
10 inopab 5007 . . 3
119, 10eqtri 2458 . 2
121, 11eqtri 2458 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653   wcel 1726  cvv 2958   cin 3321  copab 4267   cxp 4878   cres 4882 This theorem is referenced by:  resopab2  5192  opabresid  5196  mptpreima  5365  isarep2  5535  resoprab  6168  df1st2  6435  df2nd2  6436 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-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  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-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269  df-xp 4886  df-rel 4887  df-res 4892
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