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Theorem reliun 4954
 Description: An indexed union is a relation iff each member of its indexed family is a relation. (Contributed by NM, 19-Dec-2008.)
Assertion
Ref Expression
reliun

Proof of Theorem reliun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 4280 . . 3
21releqi 4918 . 2
3 df-rel 4841 . 2
4 abss 3498 . . 3
5 df-rel 4841 . . . . . 6
6 dfss2 3421 . . . . . 6
75, 6bitri 253 . . . . 5
87ralbii 2819 . . . 4
9 ralcom4 3066 . . . 4
10 r19.23v 2867 . . . . 5
1110albii 1691 . . . 4
128, 9, 113bitri 275 . . 3
134, 12bitr4i 256 . 2
142, 3, 133bitri 275 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1442   wcel 1887  cab 2437  wral 2737  wrex 2738  cvv 3045   wss 3404  ciun 4278   cxp 4832   wrel 4839 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-v 3047  df-in 3411  df-ss 3418  df-iun 4280  df-rel 4841 This theorem is referenced by:  reluni  4956  eliunxp  4972  opeliunxp2  4973  dfco2  5334  coiun  5345  fvn0ssdmfun  6013  opeliunxp2f  6956  fsumcom2  13835  fprodcom2  14038  imasaddfnlem  15434  imasvscafn  15443  gsum2d2lem  17605  gsum2d2  17606  gsumcom2  17607  dprd2d2  17677  cnextrel  21078  reldv  22825  dfcnv2  28279  cvmliftlem1  30008  cnviun  36242  coiun1  36244  eliunxp2  40168
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