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Theorem reliun 4588
 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 3754 . . 3
21releqi 4550 . 2
3 df-rel 4474 . 2
4 abss 3105 . . 3
5 df-rel 4474 . . . . . 6
6 dfss2 3028 . . . . . 6
75, 6bitri 183 . . . . 5
87ralbii 2395 . . . 4
9 ralcom4 2655 . . . 4
10 r19.23v 2494 . . . . 5
1110albii 1411 . . . 4
128, 9, 113bitri 205 . . 3
134, 12bitr4i 186 . 2
142, 3, 133bitri 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1294   wcel 1445  cab 2081  wral 2370  wrex 2371  cvv 2633   wss 3013  ciun 3752   cxp 4465   wrel 4472 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rex 2376  df-v 2635  df-in 3019  df-ss 3026  df-iun 3754  df-rel 4474 This theorem is referenced by:  reluni  4590  eliunxp  4606  opeliunxp2  4607  dfco2  4964  coiun  4974  opeliunxp2f  6041  fisumcom2  10981
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