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Theorem riin0 3884
 Description: Relative intersection of an empty family. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
riin0
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem riin0
StepHypRef Expression
1 iineq1 3827 . . 3
21ineq2d 3277 . 2
3 0iin 3871 . . . 4
43ineq2i 3274 . . 3
5 inv1 3399 . . 3
64, 5eqtri 2160 . 2
72, 6syl6eq 2188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331  cvv 2686   cin 3070  c0 3363  ciin 3814 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-in1 603  ax-in2 604  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 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-nul 3364  df-iin 3816 This theorem is referenced by: (None)
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