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Mirrors > Home > NFE Home > Th. List > difex | Unicode version |
Description: The difference of two sets is a set. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
boolex.1 | |
boolex.2 |
Ref | Expression |
---|---|
difex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | boolex.1 | . 2 | |
2 | boolex.2 | . 2 | |
3 | difexg 4102 | . 2 | |
4 | 1, 2, 3 | mp2an 653 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1710 cvv 2859 cdif 3206 |
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 df-compl 3212 df-in 3213 df-dif 3215 |
This theorem is referenced by: pwadjoin 4119 addcexlem 4382 nncex 4396 nnsucelrlem1 4424 nnsucelr 4428 ltfinex 4464 ssfin 4470 ncfinraiselem2 4480 ncfinlowerlem1 4482 tfinrelkex 4487 evenfinex 4503 oddfinex 4504 evenodddisjlem1 4515 nnadjoinlem1 4519 nnpweqlem1 4522 srelkex 4525 sfintfinlem1 4531 tfinnnlem1 4533 sfinltfin 4535 spfinex 4537 vfinspnn 4541 phialllem2 4617 phiall 4618 mpt2exlem 5811 funsex 5828 transex 5910 antisymex 5912 connexex 5913 foundex 5914 extex 5915 symex 5916 enadj 6060 ltcex 6116 2p1e3c 6156 sbthlem1 6203 dflec2 6210 nchoicelem11 6299 nchoicelem16 6304 |
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