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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 2744 | . . . 4 | |
2 | elisset 2744 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | eeanv 1925 | . . 3 | |
5 | 3, 4 | sylibr 133 | . 2 |
6 | nfv 1521 | . . . . 5 | |
7 | spc2ed.x | . . . . 5 | |
8 | 6, 7 | nfan 1558 | . . . 4 |
9 | nfv 1521 | . . . . . 6 | |
10 | spc2ed.y | . . . . . 6 | |
11 | 9, 10 | nfan 1558 | . . . . 5 |
12 | anass 399 | . . . . . . . 8 | |
13 | ancom 264 | . . . . . . . . 9 | |
14 | 13 | anbi1i 455 | . . . . . . . 8 |
15 | 12, 14 | bitr3i 185 | . . . . . . 7 |
16 | spc2ed.1 | . . . . . . . 8 | |
17 | 16 | biimparc 297 | . . . . . . 7 |
18 | 15, 17 | sylbir 134 | . . . . . 6 |
19 | 18 | ex 114 | . . . . 5 |
20 | 11, 19 | eximd 1605 | . . . 4 |
21 | 8, 20 | eximd 1605 | . . 3 |
22 | 21 | impancom 258 | . 2 |
23 | 5, 22 | sylan2 284 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wnf 1453 wex 1485 wcel 2141 |
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-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-v 2732 |
This theorem is referenced by: cnvoprab 6210 |
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