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Mirrors > Home > ILE Home > Th. List > ceqsex2 | 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 982 |
. . . . 5
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2 | 1 | exbii 1605 |
. . . 4
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3 | 19.42v 1906 |
. . . 4
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4 | 2, 3 | bitri 184 |
. . 3
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5 | 4 | exbii 1605 |
. 2
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6 | nfv 1528 |
. . . . 5
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7 | ceqsex2.1 |
. . . . 5
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8 | 6, 7 | nfan 1565 |
. . . 4
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9 | 8 | nfex 1637 |
. . 3
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10 | ceqsex2.3 |
. . 3
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11 | ceqsex2.5 |
. . . . 5
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12 | 11 | anbi2d 464 |
. . . 4
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13 | 12 | exbidv 1825 |
. . 3
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14 | 9, 10, 13 | ceqsex 2775 |
. 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 2775 |
. 2
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19 | 5, 14, 18 | 3bitri 206 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-v 2739 |
This theorem is referenced by: ceqsex2v 2778 |
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