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Theorem opabbrex 5815
 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 3990 . . 3
2 opabbrex.2 . . 3
31, 2eqeltrrid 2227 . 2
4 df-opab 3990 . . 3
5 opabbrex.1 . . . . . . 7
65adantrd 277 . . . . . 6
76anim2d 335 . . . . 5
872eximdv 1854 . . . 4
98ss2abdv 3170 . . 3
104, 9eqsstrid 3143 . 2
113, 10ssexd 4068 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  wex 1468   wcel 1480  cab 2125  cvv 2686  cop 3530   class class class wbr 3929  copab 3988  (class class class)co 5774 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084  df-opab 3990 This theorem is referenced by: (None)
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