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Mirrors > Home > ILE Home > Th. List > iotaval | Unicode version |
Description: Theorem 8.19 in [Quine] p. 57. This theorem is the fundamental property of iota. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotaval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfiota2 4868 | . 2 | |
2 | vex 2560 | . . . . . . 7 | |
3 | sbeqalb 2815 | . . . . . . . 8 | |
4 | equcomi 1592 | . . . . . . . 8 | |
5 | 3, 4 | syl6 29 | . . . . . . 7 |
6 | 2, 5 | ax-mp 7 | . . . . . 6 |
7 | 6 | ex 108 | . . . . 5 |
8 | equequ2 1599 | . . . . . . . . . 10 | |
9 | 8 | equcoms 1594 | . . . . . . . . 9 |
10 | 9 | bibi2d 221 | . . . . . . . 8 |
11 | 10 | biimpd 132 | . . . . . . 7 |
12 | 11 | alimdv 1759 | . . . . . 6 |
13 | 12 | com12 27 | . . . . 5 |
14 | 7, 13 | impbid 120 | . . . 4 |
15 | 14 | alrimiv 1754 | . . 3 |
16 | uniabio 4877 | . . 3 | |
17 | 15, 16 | syl 14 | . 2 |
18 | 1, 17 | syl5eq 2084 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wcel 1393 cab 2026 cvv 2557 cuni 3580 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-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: iotauni 4879 iota1 4881 euiotaex 4883 iota4 4885 iota5 4887 |
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