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Theorem reliin 4988
 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 4134 . 2
2 df-rel 4877 . . 3
32rexbii 2722 . 2
4 df-rel 4877 . 2
51, 3, 43imtr4i 258 1
 Colors of variables: wff set class Syntax hints:   wi 4  wrex 2698  cvv 2948   wss 3312  ciin 4086   cxp 4868   wrel 4875 This theorem is referenced by:  relint  4990  xpiindi  5002  dibglbN  31901  dihglbcpreN  32035 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-iin 4088  df-rel 4877
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