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Mirrors > Home > NFE Home > Th. List > ssdif2d | Unicode version |
Description: If is contained in and is contained in , then is contained in . Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
ssdifd.1 | |
ssdif2d.2 |
Ref | Expression |
---|---|
ssdif2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssdif2d.2 | . . 3 | |
2 | 1 | sscond 3403 | . 2 |
3 | ssdifd.1 | . . 3 | |
4 | 3 | ssdifd 3402 | . 2 |
5 | 2, 4 | sstrd 3282 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 cdif 3206 wss 3257 |
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-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-ss 3259 |
This theorem is referenced by: (None) |
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