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Theorem relun 4668
 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 3257 . 2
2 df-rel 4558 . . 3
3 df-rel 4558 . . 3
42, 3anbi12i 456 . 2
5 df-rel 4558 . 2
61, 4, 53bitr4ri 212 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  cvv 2691   cun 3076   wss 3078   cxp 4549   wrel 4556 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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1738  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-un 3082  df-in 3084  df-ss 3091  df-rel 4558 This theorem is referenced by:  funun  5179
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