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Theorem relun 5026
 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 3510 . 2
2 df-rel 4920 . . 3
3 df-rel 4920 . . 3
42, 3anbi12i 680 . 2
5 df-rel 4920 . 2
61, 4, 53bitr4ri 271 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  cvv 2965   cun 3307   wss 3309   cxp 4911   wrel 4918 This theorem is referenced by:  funun  5530  difxp  6416 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-v 2967  df-un 3314  df-in 3316  df-ss 3323  df-rel 4920
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