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Mirrors > Home > ILE Home > Th. List > spc2ed | Unicode version |
Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by Thierry Arnoux, 23-Aug-2017.) |
Ref | Expression |
---|---|
spc2ed.x | |
spc2ed.y | |
spc2ed.1 |
Ref | Expression |
---|---|
spc2ed |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2613 | . . . 4 | |
2 | elisset 2613 | . . . 4 | |
3 | 1, 2 | anim12i 331 | . . 3 |
4 | eeanv 1848 | . . 3 | |
5 | 3, 4 | sylibr 132 | . 2 |
6 | nfv 1461 | . . . . 5 | |
7 | spc2ed.x | . . . . 5 | |
8 | 6, 7 | nfan 1497 | . . . 4 |
9 | nfv 1461 | . . . . . 6 | |
10 | spc2ed.y | . . . . . 6 | |
11 | 9, 10 | nfan 1497 | . . . . 5 |
12 | anass 393 | . . . . . . . 8 | |
13 | ancom 262 | . . . . . . . . 9 | |
14 | 13 | anbi1i 445 | . . . . . . . 8 |
15 | 12, 14 | bitr3i 184 | . . . . . . 7 |
16 | spc2ed.1 | . . . . . . . 8 | |
17 | 16 | biimparc 293 | . . . . . . 7 |
18 | 15, 17 | sylbir 133 | . . . . . 6 |
19 | 18 | ex 113 | . . . . 5 |
20 | 11, 19 | eximd 1543 | . . . 4 |
21 | 8, 20 | eximd 1543 | . . 3 |
22 | 21 | impancom 256 | . 2 |
23 | 5, 22 | sylan2 280 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wex 1421 wcel 1433 |
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-7 1377 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-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: cnvoprab 5875 |
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