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Theorem reliin 5129
Description: An indexed intersection is a relation if at least one of the member of the indexed family is a relation. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
reliin

Proof of Theorem reliin
StepHypRef Expression
1 iinss 4381 . 2
2 df-rel 5011 . . 3
32rexbii 2959 . 2
4 df-rel 5011 . 2
51, 3, 43imtr4i 266 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  E.wrex 2808   cvv 3109  C_wss 3475  |^|_ciin 4331  X.cxp 5002  Relwrel 5009
This theorem is referenced by:  relint  5131  xpiindi  5143  dibglbN  36893  dihglbcpreN  37027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-iin 4333  df-rel 5011
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