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Theorem opabbrex 5549
 Description: A collection of ordered pairs with an extension of a binary relation is a set. (Contributed by Alexander van der Vekens, 1-Nov-2017.)
Hypotheses
Ref Expression
opabbrex.1
opabbrex.2
Assertion
Ref Expression
opabbrex
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem opabbrex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 3819 . . 3
2 opabbrex.2 . . 3
31, 2syl5eqelr 2125 . 2
4 df-opab 3819 . . 3
5 opabbrex.1 . . . . . . 7
65adantrd 264 . . . . . 6
76anim2d 320 . . . . 5
872eximdv 1762 . . . 4
98ss2abdv 3013 . . 3
104, 9syl5eqss 2989 . 2
113, 10ssexd 3897 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243  wex 1381   wcel 1393  cab 2026  cvv 2557  cop 3378   class class class wbr 3764  copab 3817  (class class class)co 5512 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-opab 3819 This theorem is referenced by:  sprmpt2  5857
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