Metamath Proof Explorer
Description: If a set is closed under the union of two sets, then it is closed under
finite union. (Contributed by Glauco Siliprandi, 17-Aug-2020)
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Ref |
Expression |
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Hypotheses |
fiunicl.1 |
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fiunicl.2 |
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fiunicl.3 |
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Assertion |
fiunicl |
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Proof
Step |
Hyp |
Ref |
Expression |
1 |
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fiunicl.1 |
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2 |
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fiunicl.2 |
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3 |
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fiunicl.3 |
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4 |
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uniiun |
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5 |
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nfv |
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6 |
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simpr |
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7 |
5 6 1 2 3
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fiiuncl |
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8 |
4 7
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eqeltrid |
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