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Mirrors > Home > ILE Home > Th. List > iindif2m | Unicode version |
Description: Indexed intersection of class difference. Compare to Theorem "De Morgan's laws" in [Enderton] p. 31. (Contributed by Jim Kingdon, 17-Aug-2018.) |
Ref | Expression |
---|---|
iindif2m |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.28mv 3334 | . . . 4 | |
2 | eldif 2982 | . . . . . 6 | |
3 | 2 | bicomi 130 | . . . . 5 |
4 | 3 | ralbii 2372 | . . . 4 |
5 | ralnex 2358 | . . . . . 6 | |
6 | eliun 3682 | . . . . . 6 | |
7 | 5, 6 | xchbinxr 640 | . . . . 5 |
8 | 7 | anbi2i 444 | . . . 4 |
9 | 1, 4, 8 | 3bitr3g 220 | . . 3 |
10 | vex 2604 | . . . 4 | |
11 | eliin 3683 | . . . 4 | |
12 | 10, 11 | ax-mp 7 | . . 3 |
13 | eldif 2982 | . . 3 | |
14 | 9, 12, 13 | 3bitr4g 221 | . 2 |
15 | 14 | eqrdv 2079 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 wral 2348 wrex 2349 cvv 2601 cdif 2970 ciun 3678 ciin 3679 |
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 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-iun 3680 df-iin 3681 |
This theorem is referenced by: (None) |
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