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Theorem cnvun 5244
 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 4853 . . 3
2 unopab 4252 . . . 4
3 brun 4226 . . . . 5
43opabbii 4240 . . . 4
52, 4eqtr4i 2435 . . 3
61, 5eqtr4i 2435 . 2
7 df-cnv 4853 . . 3
8 df-cnv 4853 . . 3
97, 8uneq12i 3467 . 2
106, 9eqtr4i 2435 1
 Colors of variables: wff set class Syntax hints:   wo 358   wceq 1649   cun 3286   class class class wbr 4180  copab 4233  ccnv 4844 This theorem is referenced by:  rnun  5247  f1oun  5661  f1oprswap  5684  sbthlem8  7191  domss2  7233  1sdom  7278  fpwwe2lem13  8481  strlemor1  13519  xpsc  13745  gsumzaddlem  15489  mbfres2  19498  constr2spthlem1  21555  constr3pthlem2  21604  ex-cnv  21706  funsnfsup  26641 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-un 3293  df-br 4181  df-opab 4235  df-cnv 4853
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