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Theorem cnvun 4993
 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
StepHypRef Expression
1 df-cnv 4596 . . 3
2 unopab 3992 . . . 4
3 brun 3966 . . . . 5
43opabbii 3980 . . . 4
52, 4eqtr4i 2276 . . 3
61, 5eqtr4i 2276 . 2
7 df-cnv 4596 . . 3
8 df-cnv 4596 . . 3
97, 8uneq12i 3237 . 2
106, 9eqtr4i 2276 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1619   cun 3076   class class class wbr 3920  copab 3973  ccnv 4579 This theorem is referenced by:  rnun  4996  f1oun  5349  f1oprswap  5372  sbthlem8  6863  domss2  6905  1sdom  6950  fpwwe2lem13  8144  strlemor1  13109  xpsc  13333  gsumzaddlem  15038  mbfres2  18832  ex-cnv  20637  funsnfsup  25928 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-br 3921  df-opab 3975  df-cnv 4596
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