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Mirrors > Home > NFE Home > Th. List > elcomplg | Unicode version |
Description: Membership in class complement. (Contributed by SF, 10-Jan-2015.) |
Ref | Expression |
---|---|
elcomplg | ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-compl 3212 | . . 3 ∼ &ncap | |
2 | 1 | eleq2i 2417 | . 2 ∼ &ncap |
3 | elning 3217 | . . 3 &ncap | |
4 | df-nan 1288 | . . . 4 | |
5 | anidm 625 | . . . 4 | |
6 | 4, 5 | xchbinx 301 | . . 3 |
7 | 3, 6 | syl6bb 252 | . 2 &ncap |
8 | 2, 7 | syl5bb 248 | 1 ∼ |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wa 358 wnan 1287 wcel 1710 &ncap cnin 3204 ∼ ccompl 3205 |
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 df-compl 3212 |
This theorem is referenced by: elin 3219 elun 3220 eldif 3221 elcompl 3225 nnadjoinpw 4521 nmembers1lem3 6270 |
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