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Theorem opelcnvg 4515
 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 3768 . . 3
2 breq1 3767 . . 3
3 df-cnv 4353 . . 3
41, 2, 3brabg 4006 . 2
5 df-br 3765 . 2
6 df-br 3765 . 2
74, 5, 63bitr3g 211 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wcel 1393  cop 3378   class class class wbr 3764  ccnv 4344 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-cnv 4353 This theorem is referenced by:  brcnvg  4516  opelcnv  4517  fvimacnv  5282  cnvf1olem  5845  brtposg  5869  xrlenlt  7084
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