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Mirrors > Home > NFE Home > Th. List > nincom | Unicode version |
Description: Anti-intersection commutes. (Contributed by SF, 10-Jan-2015.) |
Ref | Expression |
---|---|
nincom | &ncap &ncap |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nancom 1290 | . . 3 | |
2 | vex 2862 | . . . 4 | |
3 | 2 | elnin 3224 | . . 3 &ncap |
4 | 2 | elnin 3224 | . . 3 &ncap |
5 | 1, 3, 4 | 3bitr4i 268 | . 2 &ncap &ncap |
6 | 5 | eqriv 2350 | 1 &ncap &ncap |
Colors of variables: wff setvar class |
Syntax hints: wnan 1287 wceq 1642 wcel 1710 &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 |
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: nineq2 3235 |
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