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Mirrors > Home > ILE Home > Th. List > ceqsalt | Unicode version |
Description: Closed theorem version of ceqsalg 2582. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsalt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2568 | . . . 4 | |
2 | 1 | 3ad2ant3 927 | . . 3 |
3 | bi1 111 | . . . . . . 7 | |
4 | 3 | imim3i 55 | . . . . . 6 |
5 | 4 | al2imi 1347 | . . . . 5 |
6 | 5 | 3ad2ant2 926 | . . . 4 |
7 | 19.23t 1567 | . . . . 5 | |
8 | 7 | 3ad2ant1 925 | . . . 4 |
9 | 6, 8 | sylibd 138 | . . 3 |
10 | 2, 9 | mpid 37 | . 2 |
11 | bi2 121 | . . . . . . 7 | |
12 | 11 | imim2i 12 | . . . . . 6 |
13 | 12 | com23 72 | . . . . 5 |
14 | 13 | alimi 1344 | . . . 4 |
15 | 14 | 3ad2ant2 926 | . . 3 |
16 | 19.21t 1474 | . . . 4 | |
17 | 16 | 3ad2ant1 925 | . . 3 |
18 | 15, 17 | mpbid 135 | . 2 |
19 | 10, 18 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wal 1241 wceq 1243 wnf 1349 wex 1381 wcel 1393 |
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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 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-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: ceqsralt 2581 |
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