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Theorem cnvcnv3 5454
 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 5007 . 2
2 vex 3116 . . . 4
3 vex 3116 . . . 4
42, 3brcnv 5183 . . 3
54opabbii 4511 . 2
61, 5eqtri 2496 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1379   class class class wbr 4447  copab 4504  ccnv 4998 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-cnv 5007 This theorem is referenced by:  dfrel4v  5456
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