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Theorem cnvun 4759
 Description: The converse of a union is the union of converses. Theorem 16 of [Suppes] p. 62. (Contributed by NM, 25-Mar-1998.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
cnvun

Proof of Theorem cnvun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-cnv 4379 . . 3
2 unopab 3865 . . . 4
3 brun 3839 . . . . 5
43opabbii 3853 . . . 4
52, 4eqtr4i 2105 . . 3
61, 5eqtr4i 2105 . 2
7 df-cnv 4379 . . 3
8 df-cnv 4379 . . 3
97, 8uneq12i 3125 . 2
106, 9eqtr4i 2105 1
 Colors of variables: wff set class Syntax hints:   wo 662   wceq 1285   cun 2972   class class class wbr 3793  copab 3846  ccnv 4370 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-br 3794  df-opab 3848  df-cnv 4379 This theorem is referenced by:  rnun  4762  f1oun  5177
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