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Theorem opelcnvg 5014
 Description: Ordered-pair membership in converse. (Contributed by NM, 13-May-1999.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
opelcnvg

Proof of Theorem opelcnvg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq2 4406 . . 3
2 breq1 4405 . . 3
3 df-cnv 4842 . . 3
41, 2, 3brabg 4720 . 2
5 df-br 4403 . 2
6 df-br 4403 . 2
74, 5, 63bitr3g 291 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   wcel 1887  cop 3974   class class class wbr 4402  ccnv 4833 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403  df-opab 4462  df-cnv 4842 This theorem is referenced by:  brcnvg  5015  opelcnv  5016  elpredim  5392  fvimacnv  5997  brtpos  6982  xrlenlt  9699  brcolinear2  30825
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