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Mirrors > Home > ILE Home > Th. List > iota1 | Unicode version |
Description: Property of iota. (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
iota1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 1903 | . 2 | |
2 | sp 1401 | . . . . 5 | |
3 | iotaval 4878 | . . . . . 6 | |
4 | 3 | eqeq2d 2051 | . . . . 5 |
5 | 2, 4 | bitr4d 180 | . . . 4 |
6 | eqcom 2042 | . . . 4 | |
7 | 5, 6 | syl6bb 185 | . . 3 |
8 | 7 | exlimiv 1489 | . 2 |
9 | 1, 8 | sylbi 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wceq 1243 wex 1381 weu 1900 cio 4865 |
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-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-sn 3381 df-pr 3382 df-uni 3581 df-iota 4867 |
This theorem is referenced by: iota2df 4891 sniota 4894 tz6.12-1 5200 riota1 5486 riota1a 5487 erovlem 6198 |
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