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Mirrors > Home > ILE Home > Th. List > exse2 | Unicode version |
Description: Any set relation is set-like. (Contributed by Mario Carneiro, 22-Jun-2015.) |
Ref | Expression |
---|---|
exse2 | Se |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2315 | . . . . 5 | |
2 | vex 2560 | . . . . . . . 8 | |
3 | vex 2560 | . . . . . . . 8 | |
4 | 2, 3 | breldm 4539 | . . . . . . 7 |
5 | 4 | adantl 262 | . . . . . 6 |
6 | 5 | abssi 3015 | . . . . 5 |
7 | 1, 6 | eqsstri 2975 | . . . 4 |
8 | dmexg 4596 | . . . 4 | |
9 | ssexg 3896 | . . . 4 | |
10 | 7, 8, 9 | sylancr 393 | . . 3 |
11 | 10 | ralrimivw 2393 | . 2 |
12 | df-se 4070 | . 2 Se | |
13 | 11, 12 | sylibr 137 | 1 Se |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wcel 1393 cab 2026 wral 2306 crab 2310 cvv 2557 wss 2917 class class class wbr 3764 Se wse 4066 cdm 4345 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-rab 2315 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-se 4070 df-cnv 4353 df-dm 4355 df-rn 4356 |
This theorem is referenced by: (None) |
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