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Theorem opabid2 4969
 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 3034 . . . 4
2 vex 3034 . . . 4
3 opeq1 4158 . . . . 5
43eleq1d 2533 . . . 4
5 opeq2 4159 . . . . 5
65eleq1d 2533 . . . 4
71, 2, 4, 6opelopab 4723 . . 3
87gen2 1678 . 2
9 relopab 4965 . . 3
10 eqrel 4929 . . 3
119, 10mpan 684 . 2
128, 11mpbiri 241 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450   wceq 1452   wcel 1904  cop 3965  copab 4453   wrel 4844 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455  df-xp 4845  df-rel 4846 This theorem is referenced by:  opabbi2dv  4989
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