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Mirrors > Home > ILE Home > Th. List > seex | Unicode version |
Description: The -preimage of an element of the base set in a set-like relation is a set. (Contributed by Mario Carneiro, 19-Nov-2014.) |
Ref | Expression |
---|---|
seex | Se |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-se 4070 | . 2 Se | |
2 | breq2 3768 | . . . . 5 | |
3 | 2 | rabbidv 2549 | . . . 4 |
4 | 3 | eleq1d 2106 | . . 3 |
5 | 4 | rspccva 2655 | . 2 |
6 | 1, 5 | sylanb 268 | 1 Se |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 wral 2306 crab 2310 cvv 2557 class class class wbr 3764 Se wse 4066 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rab 2315 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-se 4070 |
This theorem is referenced by: sefvex 5196 |
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