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Mirrors > Home > ILE Home > Th. List > rspc2gv | Unicode version |
Description: Restricted specialization with two quantifiers, using implicit substitution. (Contributed by BJ, 2-Dec-2021.) |
Ref | Expression |
---|---|
rspc2gv.1 |
Ref | Expression |
---|---|
rspc2gv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2453 | . 2 | |
2 | df-ral 2453 | . . . . 5 | |
3 | 2 | imbi2i 225 | . . . 4 |
4 | 3 | albii 1463 | . . 3 |
5 | 19.21v 1866 | . . . . . 6 | |
6 | 5 | bicomi 131 | . . . . 5 |
7 | 6 | albii 1463 | . . . 4 |
8 | impexp 261 | . . . . . . 7 | |
9 | eleq1 2233 | . . . . . . . . 9 | |
10 | eleq1 2233 | . . . . . . . . 9 | |
11 | 9, 10 | bi2anan9 601 | . . . . . . . 8 |
12 | rspc2gv.1 | . . . . . . . 8 | |
13 | 11, 12 | imbi12d 233 | . . . . . . 7 |
14 | 8, 13 | bitr3id 193 | . . . . . 6 |
15 | 14 | spc2gv 2821 | . . . . 5 |
16 | 15 | pm2.43a 51 | . . . 4 |
17 | 7, 16 | syl5bi 151 | . . 3 |
18 | 4, 17 | syl5bi 151 | . 2 |
19 | 1, 18 | syl5bi 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wceq 1348 wcel 2141 wral 2448 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-ral 2453 df-v 2732 |
This theorem is referenced by: difinfsnlem 7073 difinfsn 7074 seqvalcd 10404 seqovcd 10408 qtopbasss 13276 apdiff 14042 |
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