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Theorem rintm 3744
 Description: Relative intersection of an inhabited class. (Contributed by Jim Kingdon, 19-Aug-2018.)
Assertion
Ref Expression
rintm
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rintm
StepHypRef Expression
1 incom 3129 . 2
2 intssuni2m 3639 . . . 4
3 ssid 2964 . . . . 5
4 sspwuni 3739 . . . . 5
53, 4mpbi 133 . . . 4
62, 5syl6ss 2957 . . 3
7 df-ss 2931 . . 3
86, 7sylib 127 . 2
91, 8syl5eq 2084 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243  wex 1381   wcel 1393   cin 2916   wss 2917  cpw 3359  cuni 3580  cint 3615 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-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-pw 3361  df-uni 3581  df-int 3616 This theorem is referenced by: (None)
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