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Theorem reliin 4656
 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 3859 . 2
2 df-rel 4541 . . 3
32rexbii 2440 . 2
4 df-rel 4541 . 2
51, 3, 43imtr4i 200 1
 Colors of variables: wff set class Syntax hints:   wi 4  wrex 2415  cvv 2681   wss 3066  ciin 3809   cxp 4532   wrel 4539 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-in 3072  df-ss 3079  df-iin 3811  df-rel 4541 This theorem is referenced by:  relint  4658  xpiindim  4671
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