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Theorem iundif2ss 3722
 Description: Indexed union of class difference. Compare to theorem "De Morgan's laws" in [Enderton] p. 31. (Contributed by Jim Kingdon, 17-Aug-2018.)
Assertion
Ref Expression
iundif2ss
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iundif2ss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eldif 2927 . . . . . 6
21rexbii 2331 . . . . 5
3 r19.42v 2467 . . . . 5
42, 3bitri 173 . . . 4
5 rexnalim 2317 . . . . . 6
6 vex 2560 . . . . . . 7
7 eliin 3662 . . . . . . 7
86, 7ax-mp 7 . . . . . 6
95, 8sylnibr 602 . . . . 5
109anim2i 324 . . . 4
114, 10sylbi 114 . . 3
12 eliun 3661 . . 3
13 eldif 2927 . . 3
1411, 12, 133imtr4i 190 . 2
1514ssriv 2949 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wb 98   wcel 1393  wral 2306  wrex 2307  cvv 2557   cdif 2914   wss 2917  ciun 3657  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-in1 544  ax-in2 545  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-fal 1249  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-dif 2920  df-in 2924  df-ss 2931  df-iun 3659  df-iin 3660 This theorem is referenced by: (None)
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