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Theorem relun 4454
 Description: The union of two relations is a relation. Compare Exercise 5 of [TakeutiZaring] p. 25. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
relun

Proof of Theorem relun
StepHypRef Expression
1 unss 3117 . 2
2 df-rel 4352 . . 3
3 df-rel 4352 . . 3
42, 3anbi12i 433 . 2
5 df-rel 4352 . 2
61, 4, 53bitr4ri 202 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  cvv 2557   cun 2915   wss 2917   cxp 4343   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-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-rel 4352 This theorem is referenced by:  funun  4944
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