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Theorem rnopab 5107
 Description: The range of a class of ordered pairs. (Contributed by NM, 14-Aug-1995.) (Revised by Mario Carneiro, 4-Dec-2016.)
Assertion
Ref Expression
rnopab
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem rnopab
StepHypRef Expression
1 nfopab1 4266 . . 3
2 nfopab2 4267 . . 3
31, 2dfrnf 5100 . 2
4 df-br 4205 . . . . 5
5 opabid 4453 . . . . 5
64, 5bitri 241 . . . 4
76exbii 1592 . . 3
87abbii 2547 . 2
93, 8eqtri 2455 1
 Colors of variables: wff set class Syntax hints:  wex 1550   wceq 1652   wcel 1725  cab 2421  cop 3809   class class class wbr 4204  copab 4257   crn 4871 This theorem is referenced by:  rnmpt  5108  mptpreima  5355  rnoprab  6148  marypha2lem4  7435  hartogslem1  7503  axdc2lem  8320  abrexdomjm  23980  abrexexd  23982  abrexdom  26423 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-cnv 4878  df-dm 4880  df-rn 4881
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