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Theorem cnvun 4912
 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 4515 . . 3
2 unopab 3975 . . . 4
3 brun 3947 . . . . 5
43opabbii 3963 . . . 4
52, 4eqtr4i 2139 . . 3
61, 5eqtr4i 2139 . 2
7 df-cnv 4515 . . 3
8 df-cnv 4515 . . 3
97, 8uneq12i 3196 . 2
106, 9eqtr4i 2139 1
 Colors of variables: wff set class Syntax hints:   wo 680   wceq 1314   cun 3037   class class class wbr 3897  copab 3956  ccnv 4506 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-br 3898  df-opab 3958  df-cnv 4515 This theorem is referenced by:  rnun  4915  f1oun  5353  sbthlemi8  6818  caseinj  6940  djuinj  6957
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