Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iindif2m Unicode version

Theorem iindif2m 3765
 Description: Indexed intersection of class difference. Compare to Theorem "De Morgan's laws" in [Enderton] p. 31. (Contributed by Jim Kingdon, 17-Aug-2018.)
Assertion
Ref Expression
iindif2m
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iindif2m
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 r19.28mv 3350 . . . 4
2 eldif 2991 . . . . . 6
32bicomi 130 . . . . 5
43ralbii 2377 . . . 4
5 ralnex 2363 . . . . . 6
6 eliun 3702 . . . . . 6
75, 6xchbinxr 641 . . . . 5
87anbi2i 445 . . . 4
91, 4, 83bitr3g 220 . . 3
10 vex 2613 . . . 4
11 eliin 3703 . . . 4
1210, 11ax-mp 7 . . 3
13 eldif 2991 . . 3
149, 12, 133bitr4g 221 . 2
1514eqrdv 2081 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 102   wb 103   wceq 1285  wex 1422   wcel 1434  wral 2353  wrex 2354  cvv 2610   cdif 2979  ciun 3698  ciin 3699 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-dif 2984  df-iun 3700  df-iin 3701 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator