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Theorem dfopg 3547
 Description: Value of the ordered pair when the arguments are sets. (Contributed by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
dfopg

Proof of Theorem dfopg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2566 . 2
2 elex 2566 . 2
3 df-3an 887 . . . . . 6
43baibr 829 . . . . 5
54abbidv 2155 . . . 4
6 abid2 2158 . . . 4
7 df-op 3384 . . . . 5
87eqcomi 2044 . . . 4
95, 6, 83eqtr3g 2095 . . 3
109eqcomd 2045 . 2
111, 2, 10syl2an 273 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   w3a 885   wceq 1243   wcel 1393  cab 2026  cvv 2557  csn 3375  cpr 3376  cop 3378 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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-op 3384 This theorem is referenced by:  dfop  3548  opexg  3964  opexgOLD  3965  opth1  3973  opth  3974  0nelop  3985  op1stbg  4210
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