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Mirrors > Home > ILE Home > Th. List > spc2egv | Unicode version |
Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 3-Aug-1995.) |
Ref | Expression |
---|---|
spc2egv.1 |
Ref | Expression |
---|---|
spc2egv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2700 | . . . 4 | |
2 | elisset 2700 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | eeanv 1904 | . . 3 | |
5 | 3, 4 | sylibr 133 | . 2 |
6 | spc2egv.1 | . . . 4 | |
7 | 6 | biimprcd 159 | . . 3 |
8 | 7 | 2eximdv 1854 | . 2 |
9 | 5, 8 | syl5com 29 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: spc2ev 2781 th3q 6534 addnnnq0 7257 mulnnnq0 7258 addsrpr 7553 mulsrpr 7554 |
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