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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 |
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Ref | Expression |
---|---|
spc3egv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2703 |
. . . 4
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2 | elisset 2703 |
. . . 4
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3 | elisset 2703 |
. . . 4
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4 | 1, 2, 3 | 3anim123i 1167 |
. . 3
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5 | eeeanv 1906 |
. . 3
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6 | 4, 5 | sylibr 133 |
. 2
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7 | spc3egv.1 |
. . . . 5
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8 | 7 | biimprcd 159 |
. . . 4
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9 | 8 | eximdv 1853 |
. . 3
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10 | 9 | 2eximdv 1855 |
. 2
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11 | 6, 10 | syl5com 29 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: (None) |
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