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Mirrors > Home > ILE Home > Th. List > ceqsex | Unicode version |
Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsex.1 |
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ceqsex.2 |
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ceqsex.3 |
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Ref | Expression |
---|---|
ceqsex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ceqsex.1 |
. . 3
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2 | ceqsex.3 |
. . . 4
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3 | 2 | biimpa 296 |
. . 3
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4 | 1, 3 | exlimi 1605 |
. 2
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5 | 2 | biimprcd 160 |
. . . 4
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6 | 1, 5 | alrimi 1533 |
. . 3
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7 | ceqsex.2 |
. . . 4
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8 | 7 | isseti 2760 |
. . 3
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9 | exintr 1645 |
. . 3
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10 | 6, 8, 9 | mpisyl 1457 |
. 2
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11 | 4, 10 | impbii 126 |
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 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 |
This theorem is referenced by: ceqsexv 2791 ceqsex2 2792 |
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