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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 3455 | . . . 4 | |
2 | eldif 3080 | . . . . . 6 | |
3 | 2 | bicomi 131 | . . . . 5 |
4 | 3 | ralbii 2441 | . . . 4 |
5 | ralnex 2426 | . . . . . 6 | |
6 | eliun 3817 | . . . . . 6 | |
7 | 5, 6 | xchbinxr 672 | . . . . 5 |
8 | 7 | anbi2i 452 | . . . 4 |
9 | 1, 4, 8 | 3bitr3g 221 | . . 3 |
10 | vex 2689 | . . . 4 | |
11 | eliin 3818 | . . . 4 | |
12 | 10, 11 | ax-mp 5 | . . 3 |
13 | eldif 3080 | . . 3 | |
14 | 9, 12, 13 | 3bitr4g 222 | . 2 |
15 | 14 | eqrdv 2137 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 wral 2416 wrex 2417 cvv 2686 cdif 3068 ciun 3813 ciin 3814 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-dif 3073 df-iun 3815 df-iin 3816 |
This theorem is referenced by: (None) |
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