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Mirrors > Home > ILE Home > Th. List > ssrin | Unicode version |
Description: Add right intersection to subclass relation. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ssrin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 2993 | . . . 4 | |
2 | 1 | anim1d 329 | . . 3 |
3 | elin 3155 | . . 3 | |
4 | elin 3155 | . . 3 | |
5 | 2, 3, 4 | 3imtr4g 203 | . 2 |
6 | 5 | ssrdv 3005 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wcel 1433 cin 2972 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-in 2979 df-ss 2986 |
This theorem is referenced by: sslin 3192 ss2in 3193 ssdisj 3300 ssdifin0 3324 ssres 4655 phplem2 6339 |
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