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Mirrors > Home > ILE Home > Th. List > ceqsralt | Unicode version |
Description: Restricted quantifier version of ceqsalt 2625. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsralt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2353 | . . . 4 | |
2 | eleq1 2141 | . . . . . . . . 9 | |
3 | 2 | pm5.32ri 442 | . . . . . . . 8 |
4 | 3 | imbi1i 236 | . . . . . . 7 |
5 | impexp 259 | . . . . . . 7 | |
6 | impexp 259 | . . . . . . 7 | |
7 | 4, 5, 6 | 3bitr3i 208 | . . . . . 6 |
8 | 7 | albii 1399 | . . . . 5 |
9 | 8 | a1i 9 | . . . 4 |
10 | 1, 9 | syl5bb 190 | . . 3 |
11 | 19.21v 1794 | . . 3 | |
12 | 10, 11 | syl6bb 194 | . 2 |
13 | biimt 239 | . . 3 | |
14 | 13 | 3ad2ant3 961 | . 2 |
15 | ceqsalt 2625 | . 2 | |
16 | 12, 14, 15 | 3bitr2d 214 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wal 1282 wceq 1284 wnf 1389 wcel 1433 wral 2348 |
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-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 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-3an 921 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-ral 2353 df-v 2603 |
This theorem is referenced by: ceqsralv 2630 |
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