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Mirrors > Home > ILE Home > Th. List > ceqsralt | Unicode version |
Description: Restricted quantifier version of ceqsalt 2712. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsralt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2421 | . . . 4 | |
2 | eleq1 2202 | . . . . . . . . 9 | |
3 | 2 | pm5.32ri 450 | . . . . . . . 8 |
4 | 3 | imbi1i 237 | . . . . . . 7 |
5 | impexp 261 | . . . . . . 7 | |
6 | impexp 261 | . . . . . . 7 | |
7 | 4, 5, 6 | 3bitr3i 209 | . . . . . 6 |
8 | 7 | albii 1446 | . . . . 5 |
9 | 8 | a1i 9 | . . . 4 |
10 | 1, 9 | syl5bb 191 | . . 3 |
11 | 19.21v 1845 | . . 3 | |
12 | 10, 11 | syl6bb 195 | . 2 |
13 | biimt 240 | . . 3 | |
14 | 13 | 3ad2ant3 1004 | . 2 |
15 | ceqsalt 2712 | . 2 | |
16 | 12, 14, 15 | 3bitr2d 215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wal 1329 wceq 1331 wnf 1436 wcel 1480 wral 2416 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-ral 2421 df-v 2688 |
This theorem is referenced by: ceqsralv 2717 |
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