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Mirrors > Home > ILE Home > Th. List > iota4 | Unicode version |
Description: Theorem *14.22 in [WhiteheadRussell] p. 190. (Contributed by Andrew Salmon, 12-Jul-2011.) |
Ref | Expression |
---|---|
iota4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 1903 | . 2 | |
2 | bi2 121 | . . . . . 6 | |
3 | 2 | alimi 1344 | . . . . 5 |
4 | sb2 1650 | . . . . 5 | |
5 | 3, 4 | syl 14 | . . . 4 |
6 | iotaval 4878 | . . . . . 6 | |
7 | 6 | eqcomd 2045 | . . . . 5 |
8 | dfsbcq2 2767 | . . . . 5 | |
9 | 7, 8 | syl 14 | . . . 4 |
10 | 5, 9 | mpbid 135 | . . 3 |
11 | 10 | exlimiv 1489 | . 2 |
12 | 1, 11 | sylbi 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wceq 1243 wex 1381 wsb 1645 weu 1900 wsbc 2764 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: iota4an 4886 iotacl 4890 |
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