Description: In an algebraic closure system, if S and T have the same closure and S is infinite independent, then T is infinite. This follows from applying unirnffid to the map given in acsmap2d . See Section II.5 in Cohn p. 81 to 82. (Contributed by David Moews, 1-May-2017)
Ref | Expression | ||
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Hypotheses | acsmap2d.1 | |
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acsmap2d.2 | |
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acsmap2d.3 | |
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acsmap2d.4 | |
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acsmap2d.5 | |
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acsmap2d.6 | |
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acsinfd.7 | |
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Assertion | acsinfd | |
Step | Hyp | Ref | Expression |
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1 | acsmap2d.1 | |
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2 | acsmap2d.2 | |
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3 | acsmap2d.3 | |
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4 | acsmap2d.4 | |
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5 | acsmap2d.5 | |
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6 | acsmap2d.6 | |
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7 | acsinfd.7 | |
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8 | 1 2 3 4 5 6 | acsmap2d | |
9 | simplrr | |
|
10 | simplrl | |
|
11 | inss2 | |
|
12 | fss | |
|
13 | 10 11 12 | sylancl | |
14 | simpr | |
|
15 | 13 14 | unirnffid | |
16 | 9 15 | eqeltrd | |
17 | 7 | ad2antrr | |
18 | 16 17 | pm2.65da | |
19 | 8 18 | exlimddv | |