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Mirrors > Home > ILE Home > Th. List > ceqsalt | Unicode version |
Description: Closed theorem version of ceqsalg 2709. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsalt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2695 | . . . 4 | |
2 | 1 | 3ad2ant3 1004 | . . 3 |
3 | bi1 117 | . . . . . . 7 | |
4 | 3 | imim3i 61 | . . . . . 6 |
5 | 4 | al2imi 1434 | . . . . 5 |
6 | 5 | 3ad2ant2 1003 | . . . 4 |
7 | 19.23t 1655 | . . . . 5 | |
8 | 7 | 3ad2ant1 1002 | . . . 4 |
9 | 6, 8 | sylibd 148 | . . 3 |
10 | 2, 9 | mpid 42 | . 2 |
11 | bi2 129 | . . . . . . 7 | |
12 | 11 | imim2i 12 | . . . . . 6 |
13 | 12 | com23 78 | . . . . 5 |
14 | 13 | alimi 1431 | . . . 4 |
15 | 14 | 3ad2ant2 1003 | . . 3 |
16 | 19.21t 1561 | . . . 4 | |
17 | 16 | 3ad2ant1 1002 | . . 3 |
18 | 15, 17 | mpbid 146 | . 2 |
19 | 10, 18 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wal 1329 wceq 1331 wnf 1436 wex 1468 wcel 1480 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: ceqsralt 2708 |
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