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Theorem riinm 3880
 Description: Relative intersection of an inhabited family. (Contributed by Jim Kingdon, 19-Aug-2018.)
Assertion
Ref Expression
riinm
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem riinm
StepHypRef Expression
1 incom 3263 . 2
2 r19.2m 3444 . . . . 5
32ancoms 266 . . . 4
4 iinss 3859 . . . 4
53, 4syl 14 . . 3
6 df-ss 3079 . . 3
75, 6sylib 121 . 2
81, 7syl5eq 2182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  wex 1468   wcel 1480  wral 2414  wrex 2415   cin 3065   wss 3066  ciin 3809 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 This theorem is referenced by:  riinerm  6495
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