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Theorem opelcnvg 4861
 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 4027 . . 3
2 breq1 4026 . . 3
3 df-cnv 4697 . . 3
41, 2, 3brabg 4284 . 2
5 df-br 4024 . 2
6 df-br 4024 . 2
74, 5, 63bitr3g 278 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wcel 1684  cop 3643   class class class wbr 4023  ccnv 4688 This theorem is referenced by:  brcnvg  4862  opelcnv  4863  fvimacnv  5640  brtpos  6243  xrlenlt  8890  elpredim  24176  brcolinear2  24681 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cnv 4697
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