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Theorem opabbrexOLD 6348
 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.) (Revised by BJ/AV, 20-Jun-2019.) Obsolete version of opabbrex 6347 as of 25-Mar-2020. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
opabbrexOLD

Proof of Theorem opabbrexOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 4483 . . 3
2 simpr 462 . . 3
31, 2syl5eqelr 2512 . 2
4 df-opab 4483 . . 3
5 pm3.41 561 . . . . . . . 8
65anim2d 567 . . . . . . 7
76aleximi 1698 . . . . . 6
87aleximi 1698 . . . . 5
98adantr 466 . . . 4
109ss2abdv 3534 . . 3
114, 10syl5eqss 3508 . 2
123, 11ssexd 4571 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370  wal 1435   wceq 1437  wex 1657   wcel 1872  cab 2407  cvv 3080  cop 4004   class class class wbr 4423  copab 4481 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-v 3082  df-in 3443  df-ss 3450  df-opab 4483 This theorem is referenced by: (None)
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