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Theorem resopab2 5190
 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 5187 . 2
2 ssel 3342 . . . . . 6
32pm4.71d 616 . . . . 5
43anbi1d 686 . . . 4
5 anass 631 . . . 4
64, 5syl6rbb 254 . . 3
76opabbidv 4271 . 2
81, 7syl5eq 2480 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   wss 3320  copab 4265   cres 4880 This theorem is referenced by:  resmpt  5191  marypha2lem4  7443 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267  df-xp 4884  df-rel 4885  df-res 4890
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