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Theorem relun 4709
 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 3259 . 2
2 df-rel 4595 . . 3
3 df-rel 4595 . . 3
42, 3anbi12i 681 . 2
5 df-rel 4595 . 2
61, 4, 53bitr4ri 271 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  cvv 2727   cun 3076   wss 3078   cxp 4578   wrel 4585 This theorem is referenced by:  funun  5153  difxp  6005 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-in 3085  df-ss 3089  df-rel 4595
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