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Theorem cnvco2 29043
 Description: Another distributive law of converse over class composition. (Contributed by Scott Fenton, 3-May-2014.)
Assertion
Ref Expression
cnvco2

Proof of Theorem cnvco2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 relcnv 5374 . 2
2 relco 5505 . 2
3 vex 3116 . . . . . 6
4 vex 3116 . . . . . 6
53, 4brcnv 5185 . . . . 5
6 vex 3116 . . . . . . 7
76, 4brcnv 5185 . . . . . 6
87bicomi 202 . . . . 5
95, 8anbi12ci 698 . . . 4
109exbii 1644 . . 3
116, 3opelcnv 5184 . . . 4
123, 6opelco 5174 . . . 4
1311, 12bitri 249 . . 3
146, 3opelco 5174 . . 3
1510, 13, 143bitr4i 277 . 2
161, 2, 15eqrelriiv 5097 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1379  wex 1596   wcel 1767  cop 4033   class class class wbr 4447  ccnv 4998   ccom 5003 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-ral 2819  df-rex 2820  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-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008 This theorem is referenced by: (None)
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