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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 3120 | . . . . . 6 | |
2 | 1 | rexbii 2471 | . . . . 5 |
3 | r19.42v 2621 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | rexnalim 2453 | . . . . . 6 | |
6 | vex 2724 | . . . . . . 7 | |
7 | eliin 3865 | . . . . . . 7 | |
8 | 6, 7 | ax-mp 5 | . . . . . 6 |
9 | 5, 8 | sylnibr 667 | . . . . 5 |
10 | 9 | anim2i 340 | . . . 4 |
11 | 4, 10 | sylbi 120 | . . 3 |
12 | eliun 3864 | . . 3 | |
13 | eldif 3120 | . . 3 | |
14 | 11, 12, 13 | 3imtr4i 200 | . 2 |
15 | 14 | ssriv 3141 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wb 104 wcel 2135 wral 2442 wrex 2443 cvv 2721 cdif 3108 wss 3111 ciun 3860 ciin 3861 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-dif 3113 df-in 3117 df-ss 3124 df-iun 3862 df-iin 3863 |
This theorem is referenced by: (None) |
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