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Mirrors > Home > ILE Home > Th. List > ceqsex4v | Unicode version |
Description: Elimination of four existential quantifiers, using implicit substitution. (Contributed by NM, 23-Sep-2011.) |
Ref | Expression |
---|---|
ceqsex4v.1 |
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ceqsex4v.2 |
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ceqsex4v.3 |
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ceqsex4v.4 |
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ceqsex4v.7 |
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ceqsex4v.8 |
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ceqsex4v.9 |
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ceqsex4v.10 |
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Ref | Expression |
---|---|
ceqsex4v |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.42vv 1785 |
. . . 4
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2 | 3anass 888 |
. . . . . 6
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3 | df-3an 886 |
. . . . . . 7
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4 | 3 | anbi2i 430 |
. . . . . 6
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5 | 2, 4 | bitr4i 176 |
. . . . 5
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6 | 5 | 2exbii 1494 |
. . . 4
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7 | df-3an 886 |
. . . 4
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8 | 1, 6, 7 | 3bitr4i 201 |
. . 3
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9 | 8 | 2exbii 1494 |
. 2
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10 | ceqsex4v.1 |
. . 3
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11 | ceqsex4v.2 |
. . 3
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12 | ceqsex4v.7 |
. . . . 5
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13 | 12 | 3anbi3d 1212 |
. . . 4
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14 | 13 | 2exbidv 1745 |
. . 3
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15 | ceqsex4v.8 |
. . . . 5
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16 | 15 | 3anbi3d 1212 |
. . . 4
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17 | 16 | 2exbidv 1745 |
. . 3
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18 | 10, 11, 14, 17 | ceqsex2v 2589 |
. 2
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19 | ceqsex4v.3 |
. . 3
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20 | ceqsex4v.4 |
. . 3
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21 | ceqsex4v.9 |
. . 3
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22 | ceqsex4v.10 |
. . 3
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23 | 19, 20, 21, 22 | ceqsex2v 2589 |
. 2
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24 | 9, 18, 23 | 3bitri 195 |
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-3an 886 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: ceqsex8v 2593 |
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