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Mirrors > Home > NFE Home > Th. List > ssdif0 | Unicode version |
Description: Subclass expressed in terms of difference. Exercise 7 of [TakeutiZaring] p. 22. (Contributed by NM, 29-Apr-1994.) |
Ref | Expression |
---|---|
ssdif0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iman 413 | . . . 4 | |
2 | eldif 3221 | . . . 4 | |
3 | 1, 2 | xchbinxr 302 | . . 3 |
4 | 3 | albii 1566 | . 2 |
5 | dfss2 3262 | . 2 | |
6 | eq0 3564 | . 2 | |
7 | 4, 5, 6 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wa 358 wal 1540 wceq 1642 wcel 1710 cdif 3206 wss 3257 c0 3550 |
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-ne 2518 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: vdif0 3610 pssdifn0 3611 difid 3618 difin0 3623 sfinltfin 4535 |
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