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Mirrors > Home > NFE 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 2869 | . . . 4 | |
2 | elisset 2869 | . . . 4 | |
3 | elisset 2869 | . . . 4 | |
4 | 1, 2, 3 | 3anim123i 1137 | . . 3 |
5 | eeeanv 1914 | . . 3 | |
6 | 4, 5 | sylibr 203 | . 2 |
7 | spc3egv.1 | . . . . 5 | |
8 | 7 | biimprcd 216 | . . . 4 |
9 | 8 | eximdv 1622 | . . 3 |
10 | 9 | 2eximdv 1624 | . 2 |
11 | 6, 10 | syl5com 26 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 w3a 934 wex 1541 wceq 1642 wcel 1710 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: spc3gv 2944 |
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