Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > spc3egv | Unicode version |
Description: Existential specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.) |
Ref | Expression |
---|---|
spc3egv.1 |
Ref | Expression |
---|---|
spc3egv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2674 | . . . 4 | |
2 | elisset 2674 | . . . 4 | |
3 | elisset 2674 | . . . 4 | |
4 | 1, 2, 3 | 3anim123i 1151 | . . 3 |
5 | eeeanv 1885 | . . 3 | |
6 | 4, 5 | sylibr 133 | . 2 |
7 | spc3egv.1 | . . . . 5 | |
8 | 7 | biimprcd 159 | . . . 4 |
9 | 8 | eximdv 1836 | . . 3 |
10 | 9 | 2eximdv 1838 | . 2 |
11 | 6, 10 | syl5com 29 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 947 wceq 1316 wex 1453 wcel 1465 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |