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Mirrors > Home > MPE Home > Th. List > ceqsex3v | Structured version Visualization version Unicode version |
Description: Elimination of three existential quantifiers, using implicit substitution. (Contributed by NM, 16-Aug-2011.) |
Ref | Expression |
---|---|
ceqsex3v.1 |
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ceqsex3v.2 |
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ceqsex3v.3 |
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ceqsex3v.4 |
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ceqsex3v.5 |
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ceqsex3v.6 |
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Ref | Expression |
---|---|
ceqsex3v |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 659 |
. . . . . 6
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2 | 3anass 990 |
. . . . . . 7
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3 | 2 | anbi1i 706 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | df-3an 988 |
. . . . . . 7
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5 | 4 | anbi2i 705 |
. . . . . 6
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6 | 1, 3, 5 | 3bitr4i 285 |
. . . . 5
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7 | 6 | 2exbii 1723 |
. . . 4
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8 | 19.42vv 1840 |
. . . 4
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9 | 7, 8 | bitri 257 |
. . 3
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10 | 9 | exbii 1722 |
. 2
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11 | ceqsex3v.1 |
. . . 4
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12 | ceqsex3v.4 |
. . . . . 6
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13 | 12 | 3anbi3d 1349 |
. . . . 5
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14 | 13 | 2exbidv 1774 |
. . . 4
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15 | 11, 14 | ceqsexv 3052 |
. . 3
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16 | ceqsex3v.2 |
. . . 4
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17 | ceqsex3v.3 |
. . . 4
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18 | ceqsex3v.5 |
. . . 4
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19 | ceqsex3v.6 |
. . . 4
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20 | 16, 17, 18, 19 | ceqsex2v 3055 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 15, 20 | bitri 257 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 10, 21 | bitri 257 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-11 1924 ax-12 1937 ax-ext 2432 |
This theorem depends on definitions: df-bi 190 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-clab 2439 df-cleq 2445 df-clel 2448 df-v 3015 |
This theorem is referenced by: ceqsex6v 3058 |
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