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Theorem opelcnvg 4458
Description: Ordered-pair membership in converse. (Contributed by NM, 13-May-1999.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
opelcnvg  C  D  <. ,  >.  `' R  <. ,  >.  R

Proof of Theorem opelcnvg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq2 3759 . . 3  R  R
2 breq1 3758 . . 3  R  R
3 df-cnv 4296 . . 3  `' R  { <. , 
>.  |  R }
41, 2, 3brabg 3997 . 2  C  D  `' R  R
5 df-br 3756 . 2  `' R  <. ,  >.  `' R
6 df-br 3756 . 2  R  <. ,  >.  R
74, 5, 63bitr3g 211 1  C  D  <. ,  >.  `' R  <. ,  >.  R
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wcel 1390   <.cop 3370   class class class wbr 3755   `'ccnv 4287
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-cnv 4296
This theorem is referenced by:  brcnvg  4459  opelcnv  4460  fvimacnv  5225  cnvf1olem  5787  brtposg  5810  xrlenlt  6881
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