Metamath Proof Explorer
Description: A trivial group has exactly one normal subgroup. (Contributed by Rohan
Ridenour, 3-Aug-2023)
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Ref |
Expression |
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Hypotheses |
triv1nsgd.1 |
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triv1nsgd.2 |
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triv1nsgd.3 |
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triv1nsgd.4 |
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Assertion |
triv1nsgd |
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Proof
Step |
Hyp |
Ref |
Expression |
1 |
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triv1nsgd.1 |
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2 |
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triv1nsgd.2 |
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3 |
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triv1nsgd.3 |
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4 |
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triv1nsgd.4 |
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5 |
1 2 3 4
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trivnsgd |
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6 |
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snex |
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7 |
4 6
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eqeltrdi |
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8 |
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ensn1g |
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9 |
7 8
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syl |
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10 |
5 9
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eqbrtrd |
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