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Mirrors > Home > NFE Home > Th. List > ninexg | Unicode version |
Description: The anti-intersection of two sets is a set. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
ninexg | &ncap |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nineq1 3234 | . . 3 &ncap &ncap | |
2 | 1 | eleq1d 2419 | . 2 &ncap &ncap |
3 | nineq2 3235 | . . 3 &ncap &ncap | |
4 | 3 | eleq1d 2419 | . 2 &ncap &ncap |
5 | ax-nin 4078 | . . 3 | |
6 | isset 2863 | . . . 4 &ncap &ncap | |
7 | dfcleq 2347 | . . . . . 6 &ncap &ncap | |
8 | vex 2862 | . . . . . . . . 9 | |
9 | 8 | elnin 3224 | . . . . . . . 8 &ncap |
10 | 9 | bibi2i 304 | . . . . . . 7 &ncap |
11 | 10 | albii 1566 | . . . . . 6 &ncap |
12 | 7, 11 | bitri 240 | . . . . 5 &ncap |
13 | 12 | exbii 1582 | . . . 4 &ncap |
14 | 6, 13 | bitri 240 | . . 3 &ncap |
15 | 5, 14 | mpbir 200 | . 2 &ncap |
16 | 2, 4, 15 | vtocl2g 2918 | 1 &ncap |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wnan 1287 wal 1540 wex 1541 wceq 1642 wcel 1710 cvv 2859 &ncap cnin 3204 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 |
This theorem is referenced by: ninex 4098 complexg 4099 inexg 4100 unexg 4101 |
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