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Theorem cnvun 4672
 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 4296 . . 3
2 unopab 3827 . . . 4
3 brun 3801 . . . . 5
43opabbii 3815 . . . 4
52, 4eqtr4i 2060 . . 3
61, 5eqtr4i 2060 . 2
7 df-cnv 4296 . . 3
8 df-cnv 4296 . . 3
97, 8uneq12i 3089 . 2
106, 9eqtr4i 2060 1
 Colors of variables: wff set class Syntax hints:   wo 628   wceq 1242   cun 2909   class class class wbr 3755  copab 3808  ccnv 4287 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-br 3756  df-opab 3810  df-cnv 4296 This theorem is referenced by:  rnun  4675  f1oun  5089
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