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Theorem iinin1m 3726
 Description: Indexed intersection of intersection. Compare to Theorem "Distributive laws" in [Enderton] p. 30. (Contributed by Jim Kingdon, 17-Aug-2018.)
Assertion
Ref Expression
iinin1m
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iinin1m
StepHypRef Expression
1 iinin2m 3725 . 2
2 incom 3129 . . . 4
32a1i 9 . . 3
43iineq2i 3676 . 2
5 incom 3129 . 2
61, 4, 53eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  wex 1381   wcel 1393   cin 2916  ciin 3658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-iin 3660 This theorem is referenced by: (None)
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