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Theorem resopab2 5332
 Description: Restriction of a class abstraction of ordered pairs. (Contributed by NM, 24-Aug-2007.)
Assertion
Ref Expression
resopab2
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem resopab2
StepHypRef Expression
1 resopab 5330 . 2
2 ssel 3493 . . . . . 6
32pm4.71d 634 . . . . 5
43anbi1d 704 . . . 4
5 anass 649 . . . 4
64, 5syl6rbb 262 . . 3
76opabbidv 4520 . 2
81, 7syl5eq 2510 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819   wss 3471  copab 4514   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:  resmpt  5333  marypha2lem4  7916
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