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

Theorem reluni 4702
 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 3898 . . 3
21releqi 4662 . 2
3 reliun 4700 . 2
42, 3bitri 183 1
 Colors of variables: wff set class Syntax hints:   wb 104  wral 2432  cuni 3768  ciun 3845   wrel 4584 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-in 3104  df-ss 3111  df-uni 3769  df-iun 3847  df-rel 4586 This theorem is referenced by:  fununi  5231  tfrlem6  6253
 Copyright terms: Public domain W3C validator