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Theorem reliun 4458
 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 3659 . . 3
21releqi 4423 . 2
3 df-rel 4352 . 2
4 abss 3009 . . 3
5 df-rel 4352 . . . . . 6
6 dfss2 2934 . . . . . 6
75, 6bitri 173 . . . . 5
87ralbii 2330 . . . 4
9 ralcom4 2576 . . . 4
10 r19.23v 2425 . . . . 5
1110albii 1359 . . . 4
128, 9, 113bitri 195 . . 3
134, 12bitr4i 176 . 2
142, 3, 133bitri 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wcel 1393  cab 2026  wral 2306  wrex 2307  cvv 2557   wss 2917  ciun 3657   cxp 4343   wrel 4350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-iun 3659  df-rel 4352 This theorem is referenced by:  reluni  4460  eliunxp  4475  opeliunxp2  4476  dfco2  4820  coiun  4830
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