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Mirrors > Home > ILE Home > Th. List > ceqsralt | Unicode version |
Description: Restricted quantifier version of ceqsalt 2748. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsralt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2447 | . . . 4 | |
2 | eleq1 2227 | . . . . . . . . 9 | |
3 | 2 | pm5.32ri 451 | . . . . . . . 8 |
4 | 3 | imbi1i 237 | . . . . . . 7 |
5 | impexp 261 | . . . . . . 7 | |
6 | impexp 261 | . . . . . . 7 | |
7 | 4, 5, 6 | 3bitr3i 209 | . . . . . 6 |
8 | 7 | albii 1457 | . . . . 5 |
9 | 8 | a1i 9 | . . . 4 |
10 | 1, 9 | syl5bb 191 | . . 3 |
11 | 19.21v 1860 | . . 3 | |
12 | 10, 11 | bitrdi 195 | . 2 |
13 | biimt 240 | . . 3 | |
14 | 13 | 3ad2ant3 1009 | . 2 |
15 | ceqsalt 2748 | . 2 | |
16 | 12, 14, 15 | 3bitr2d 215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 967 wal 1340 wceq 1342 wnf 1447 wcel 2135 wral 2442 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-ral 2447 df-v 2724 |
This theorem is referenced by: ceqsralv 2753 |
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