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Theorem cnvcnv3 4956
 Description: The set of all ordered pairs in a class is the same as the double converse. (Contributed by Mario Carneiro, 16-Aug-2015.)
Assertion
Ref Expression
cnvcnv3
Distinct variable group:   ,,

Proof of Theorem cnvcnv3
StepHypRef Expression
1 df-cnv 4515 . 2
2 vex 2661 . . . 4
3 vex 2661 . . . 4
42, 3brcnv 4690 . . 3
54opabbii 3963 . 2
61, 5eqtri 2136 1
 Colors of variables: wff set class Syntax hints:   wceq 1314   class class class wbr 3897  copab 3956  ccnv 4506 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066  ax-pr 4099 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-pw 3480  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898  df-opab 3958  df-cnv 4515 This theorem is referenced by:  dfrel4v  4958
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