New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > disjpss | Unicode version |
Description: A class is a proper subset of its union with a disjoint nonempty class. (Contributed by NM, 15-Sep-2004.) |
Ref | Expression |
---|---|
disjpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3290 | . . . . . . . 8 | |
2 | 1 | biantru 491 | . . . . . . 7 |
3 | ssin 3477 | . . . . . . 7 | |
4 | 2, 3 | bitri 240 | . . . . . 6 |
5 | sseq2 3293 | . . . . . 6 | |
6 | 4, 5 | syl5bb 248 | . . . . 5 |
7 | ss0 3581 | . . . . 5 | |
8 | 6, 7 | syl6bi 219 | . . . 4 |
9 | 8 | necon3ad 2552 | . . 3 |
10 | 9 | imp 418 | . 2 |
11 | nsspssun 3488 | . . 3 | |
12 | uncom 3408 | . . . 4 | |
13 | 12 | psseq2i 3359 | . . 3 |
14 | 11, 13 | bitri 240 | . 2 |
15 | 10, 14 | sylib 188 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 358 wceq 1642 wne 2516 cun 3207 cin 3208 wss 3257 wpss 3258 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-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-pss 3261 df-nul 3551 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |