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Theorem opabrn 27135
 Description: Range of an ordered-pair class abstraction. (Contributed by Thierry Arnoux, 31-Aug-2017.)
Assertion
Ref Expression
opabrn
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem opabrn
StepHypRef Expression
1 dfrn2 5189 . 2
2 nfcv 2629 . . . 4
3 nfopab2 4514 . . . 4
42, 3nfeq 2640 . . 3
5 nfcv 2629 . . . . 5
6 nfopab1 4513 . . . . 5
75, 6nfeq 2640 . . . 4
8 df-br 4448 . . . . 5
9 eleq2 2540 . . . . . 6
10 opabid 4754 . . . . . 6
119, 10syl6bb 261 . . . . 5
128, 11syl5bb 257 . . . 4
137, 12exbid 1834 . . 3
144, 13abbid 2602 . 2
151, 14syl5eq 2520 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379  wex 1596   wcel 1767  cab 2452  cop 4033   class class class wbr 4447  copab 4504   crn 5000 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-cnv 5007  df-dm 5009  df-rn 5010 This theorem is referenced by:  fpwrelmapffslem  27224
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