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Mirrors > Home > ILE Home > Th. List > ssrd | Unicode version |
Description: Deduction based on subclass definition. (Contributed by Thierry Arnoux, 8-Mar-2017.) |
Ref | Expression |
---|---|
ssrd.0 | |
ssrd.1 | |
ssrd.2 | |
ssrd.3 |
Ref | Expression |
---|---|
ssrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrd.0 | . . 3 | |
2 | ssrd.3 | . . 3 | |
3 | 1, 2 | alrimi 1502 | . 2 |
4 | ssrd.1 | . . 3 | |
5 | ssrd.2 | . . 3 | |
6 | 4, 5 | dfss2f 3083 | . 2 |
7 | 3, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wnf 1436 wcel 1480 wnfc 2266 wss 3066 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-in 3072 df-ss 3079 |
This theorem is referenced by: eqrd 3110 exmidomni 7007 |
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