Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  reluni Unicode version

Theorem reluni 4460
 Description: The union of a class is a relation iff any member is a relation. Exercise 6 of [TakeutiZaring] p. 25 and its converse. (Contributed by NM, 13-Aug-2004.)
Assertion
Ref Expression
reluni
Distinct variable group:   ,

Proof of Theorem reluni
StepHypRef Expression
1 uniiun 3710 . . 3
21releqi 4423 . 2
3 reliun 4458 . 2
42, 3bitri 173 1
 Colors of variables: wff set class Syntax hints:   wb 98  wral 2306  cuni 3580  ciun 3657   wrel 4350 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-uni 3581  df-iun 3659  df-rel 4352 This theorem is referenced by:  fununi  4967  tfrlem6  5932
 Copyright terms: Public domain W3C validator