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Theorem resopab 5330
 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 5020 . 2
2 df-xp 5014 . . . . . 6
3 vex 3112 . . . . . . . 8
43biantru 505 . . . . . . 7
54opabbii 4521 . . . . . 6
62, 5eqtr4i 2489 . . . . 5
76ineq2i 3693 . . . 4
8 incom 3687 . . . 4
97, 8eqtri 2486 . . 3
10 inopab 5143 . . 3
119, 10eqtri 2486 . 2
121, 11eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1395   wcel 1819  cvv 3109   cin 3470  copab 4514   cxp 5006   cres 5010 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-opab 4516  df-xp 5014  df-rel 5015  df-res 5020 This theorem is referenced by:  resopab2  5332  opabresid  5337  mptpreima  5506  isarep2  5674  resoprab  6397  elrnmpt2res  6415  df1st2  6885  df2nd2  6886
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