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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 2744 | . . . 4 | |
2 | elisset 2744 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | eeanv 1925 | . . 3 | |
5 | 3, 4 | sylibr 133 | . 2 |
6 | spc2egv.1 | . . . 4 | |
7 | 6 | biimprcd 159 | . . 3 |
8 | 7 | 2eximdv 1875 | . 2 |
9 | 5, 8 | syl5com 29 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 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: spc2ev 2826 th3q 6618 addnnnq0 7411 mulnnnq0 7412 addsrpr 7707 mulsrpr 7708 |
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