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Mirrors > Home > ILE Home > Th. List > iundif2ss | Unicode version |
Description: Indexed union of class difference. Compare to theorem "De Morgan's laws" in [Enderton] p. 31. (Contributed by Jim Kingdon, 17-Aug-2018.) |
Ref | Expression |
---|---|
iundif2ss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3080 | . . . . . 6 | |
2 | 1 | rexbii 2442 | . . . . 5 |
3 | r19.42v 2588 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | rexnalim 2427 | . . . . . 6 | |
6 | vex 2689 | . . . . . . 7 | |
7 | eliin 3818 | . . . . . . 7 | |
8 | 6, 7 | ax-mp 5 | . . . . . 6 |
9 | 5, 8 | sylnibr 666 | . . . . 5 |
10 | 9 | anim2i 339 | . . . 4 |
11 | 4, 10 | sylbi 120 | . . 3 |
12 | eliun 3817 | . . 3 | |
13 | eldif 3080 | . . 3 | |
14 | 11, 12, 13 | 3imtr4i 200 | . 2 |
15 | 14 | ssriv 3101 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wcel 1480 wral 2416 wrex 2417 cvv 2686 cdif 3068 wss 3071 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-in 3077 df-ss 3084 df-iun 3815 df-iin 3816 |
This theorem is referenced by: (None) |
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