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Mirrors > Home > NFE Home > Th. List > incompl | Unicode version |
Description: Intersection with complement. (Contributed by SF, 2-Jan-2018.) |
Ref | Expression |
---|---|
incompl | ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-in 3213 | . 2 ∼ ∼ &ncap ∼ | |
2 | nincompl 4072 | . . 3 &ncap ∼ | |
3 | 2 | compleqi 3244 | . 2 ∼ &ncap ∼ ∼ |
4 | complV 4070 | . 2 ∼ | |
5 | 1, 3, 4 | 3eqtri 2377 | 1 ∼ |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 cvv 2859 &ncap cnin 3204 ∼ ccompl 3205 cin 3208 c0 3550 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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 df-compl 3212 df-in 3213 df-dif 3215 df-ss 3259 df-nul 3551 |
This theorem is referenced by: inindif 4075 nnsucelrlem3 4426 vfintle 4546 vfin1cltv 4547 fnfullfun 5858 fvfullfun 5864 sbthlem1 6203 |
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