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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 1944 | . 2 | |
2 | bi2 128 | . . . . . 6 | |
3 | 2 | alimi 1384 | . . . . 5 |
4 | sb2 1690 | . . . . 5 | |
5 | 3, 4 | syl 14 | . . . 4 |
6 | iotaval 4898 | . . . . . 6 | |
7 | 6 | eqcomd 2086 | . . . . 5 |
8 | dfsbcq2 2818 | . . . . 5 | |
9 | 7, 8 | syl 14 | . . . 4 |
10 | 5, 9 | mpbid 145 | . . 3 |
11 | 10 | exlimiv 1529 | . 2 |
12 | 1, 11 | sylbi 119 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wceq 1284 wex 1421 wsb 1685 weu 1941 wsbc 2815 cio 4885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-sbc 2816 df-un 2977 df-sn 3404 df-pr 3405 df-uni 3602 df-iota 4887 |
This theorem is referenced by: iota4an 4906 iotacl 4910 |
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