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Mirrors > Home > ILE Home > Th. List > ceqsralt | Unicode version |
Description: Restricted quantifier version of ceqsalt 2580. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsralt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2311 | . . . 4 | |
2 | eleq1 2100 | . . . . . . . . 9 | |
3 | 2 | pm5.32ri 428 | . . . . . . . 8 |
4 | 3 | imbi1i 227 | . . . . . . 7 |
5 | impexp 250 | . . . . . . 7 | |
6 | impexp 250 | . . . . . . 7 | |
7 | 4, 5, 6 | 3bitr3i 199 | . . . . . 6 |
8 | 7 | albii 1359 | . . . . 5 |
9 | 8 | a1i 9 | . . . 4 |
10 | 1, 9 | syl5bb 181 | . . 3 |
11 | 19.21v 1753 | . . 3 | |
12 | 10, 11 | syl6bb 185 | . 2 |
13 | biimt 230 | . . 3 | |
14 | 13 | 3ad2ant3 927 | . 2 |
15 | ceqsalt 2580 | . 2 | |
16 | 12, 14, 15 | 3bitr2d 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wal 1241 wceq 1243 wnf 1349 wcel 1393 wral 2306 |
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-ral 2311 df-v 2559 |
This theorem is referenced by: ceqsralv 2585 |
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