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Theorem opabid2 4495
 Description: A relation expressed as an ordered pair abstraction. (Contributed by NM, 11-Dec-2006.)
Assertion
Ref Expression
opabid2
Distinct variable group:   ,,

Proof of Theorem opabid2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 2605 . . . 4
2 vex 2605 . . . 4
3 opeq1 3578 . . . . 5
43eleq1d 2148 . . . 4
5 opeq2 3579 . . . . 5
65eleq1d 2148 . . . 4
71, 2, 4, 6opelopab 4034 . . 3
87gen2 1380 . 2
9 relopab 4492 . . 3
10 eqrel 4455 . . 3
119, 10mpan 415 . 2
128, 11mpbiri 166 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283   wceq 1285   wcel 1434  cop 3409  copab 3846   wrel 4376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-opab 3848  df-xp 4377  df-rel 4378 This theorem is referenced by:  opabbi2dv  4513
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