New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > inexg | Unicode version |
Description: The intersection of two sets is a set. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
inexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-in 3213 | . 2 ∼ &ncap | |
2 | ninexg 4097 | . . 3 &ncap | |
3 | complexg 4099 | . . 3 &ncap ∼ &ncap | |
4 | 2, 3 | syl 15 | . 2 ∼ &ncap |
5 | 1, 4 | syl5eqel 2437 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wcel 1710 cvv 2859 &ncap cnin 3204 ∼ ccompl 3205 cin 3208 |
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 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 |
This theorem is referenced by: difexg 4102 inex 4105 xpkexg 4288 imakexg 4299 cokexg 4309 peano5 4409 spfininduct 4540 xpexg 5114 resexg 5116 txpexg 5784 fixexg 5788 clos1induct 5880 frds 5935 pmex 6005 nenpw1pwlem1 6084 ovcelem1 6171 fnfreclem1 6317 |
Copyright terms: Public domain | W3C validator |