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Mirrors > Home > ILE Home > Th. List > sess2 | Unicode version |
Description: Subset theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
sess2 | Se Se |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssralv 3131 | . . 3 | |
2 | rabss2 3150 | . . . . 5 | |
3 | ssexg 4037 | . . . . . 6 | |
4 | 3 | ex 114 | . . . . 5 |
5 | 2, 4 | syl 14 | . . . 4 |
6 | 5 | ralimdv 2477 | . . 3 |
7 | 1, 6 | syld 45 | . 2 |
8 | df-se 4225 | . 2 Se | |
9 | df-se 4225 | . 2 Se | |
10 | 7, 8, 9 | 3imtr4g 204 | 1 Se Se |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 wral 2393 crab 2397 cvv 2660 wss 3041 class class class wbr 3899 Se wse 4221 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rab 2402 df-v 2662 df-in 3047 df-ss 3054 df-se 4225 |
This theorem is referenced by: seeq2 4232 |
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