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Mirrors > Home > NFE 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 1907 |
. . . 4
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2 | 3anass 938 |
. . . . . 6
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3 | df-3an 936 |
. . . . . . 7
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4 | 3 | anbi2i 675 |
. . . . . 6
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5 | 2, 4 | bitr4i 243 |
. . . . 5
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6 | 5 | 2exbii 1583 |
. . . 4
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7 | df-3an 936 |
. . . 4
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8 | 1, 6, 7 | 3bitr4i 268 |
. . 3
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9 | 8 | 2exbii 1583 |
. 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 1258 |
. . . 4
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14 | 13 | 2exbidv 1628 |
. . 3
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15 | ceqsex4v.8 |
. . . . 5
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16 | 15 | 3anbi3d 1258 |
. . . 4
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17 | 16 | 2exbidv 1628 |
. . 3
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18 | 10, 11, 14, 17 | ceqsex2v 2896 |
. 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 2896 |
. 2
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24 | 9, 18, 23 | 3bitri 262 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: ceqsex8v 2900 |
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