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Mirrors > Home > MPE Home > Th. List > ceqsex2 | Structured version Visualization version Unicode version |
Description: Elimination of two existential quantifiers, using implicit substitution. (Contributed by Scott Fenton, 7-Jun-2006.) |
Ref | Expression |
---|---|
ceqsex2.1 |
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ceqsex2.2 |
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ceqsex2.3 |
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ceqsex2.4 |
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ceqsex2.5 |
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ceqsex2.6 |
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Ref | Expression |
---|---|
ceqsex2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 1011 |
. . . . 5
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2 | 1 | exbii 1726 |
. . . 4
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3 | 19.42v 1842 |
. . . 4
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4 | 2, 3 | bitri 257 |
. . 3
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5 | 4 | exbii 1726 |
. 2
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6 | nfv 1769 |
. . . . 5
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7 | ceqsex2.1 |
. . . . 5
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8 | 6, 7 | nfan 2031 |
. . . 4
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9 | 8 | nfex 2050 |
. . 3
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10 | ceqsex2.3 |
. . 3
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11 | ceqsex2.5 |
. . . . 5
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12 | 11 | anbi2d 718 |
. . . 4
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13 | 12 | exbidv 1776 |
. . 3
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14 | 9, 10, 13 | ceqsex 3069 |
. 2
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15 | ceqsex2.2 |
. . 3
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16 | ceqsex2.4 |
. . 3
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17 | ceqsex2.6 |
. . 3
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18 | 15, 16, 17 | ceqsex 3069 |
. 2
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19 | 5, 14, 18 | 3bitri 279 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-v 3033 |
This theorem is referenced by: ceqsex2v 3073 |
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