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Mirrors > Home > ILE Home > Th. List > spc2gv | Unicode version |
Description: Specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 27-Apr-2004.) |
Ref | Expression |
---|---|
spc2egv.1 |
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Ref | Expression |
---|---|
spc2gv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2562 |
. . . 4
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2 | elisset 2562 |
. . . 4
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3 | 1, 2 | anim12i 321 |
. . 3
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4 | eeanv 1804 |
. . 3
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5 | 3, 4 | sylibr 137 |
. 2
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6 | spc2egv.1 |
. . . . . 6
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7 | 6 | biimpcd 148 |
. . . . 5
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8 | 7 | 2alimi 1342 |
. . . 4
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9 | exim 1487 |
. . . . 5
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10 | 9 | alimi 1341 |
. . . 4
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11 | exim 1487 |
. . . 4
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12 | 8, 10, 11 | 3syl 17 |
. . 3
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13 | 19.9v 1748 |
. . . 4
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14 | 19.9v 1748 |
. . . 4
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15 | 13, 14 | bitri 173 |
. . 3
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16 | 12, 15 | syl6ib 150 |
. 2
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17 | 5, 16 | syl5com 26 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: trel 3852 elovmpt2 5643 |
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