Description: The "natural forgetful functor" from the category of unital rings into the category of sets which sends each ring to its underlying set (base set) and the morphisms (ring homomorphisms) to mappings of the corresponding base sets. (Contributed by AV, 16-Feb-2020) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | funcringcsetcALTV2.r | |
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funcringcsetcALTV2.s | |
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funcringcsetcALTV2.b | |
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funcringcsetcALTV2.c | |
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funcringcsetcALTV2.u | |
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funcringcsetcALTV2.f | |
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funcringcsetcALTV2.g | |
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Assertion | funcringcsetcALTV2 | |
Step | Hyp | Ref | Expression |
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1 | funcringcsetcALTV2.r | |
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2 | funcringcsetcALTV2.s | |
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3 | funcringcsetcALTV2.b | |
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4 | funcringcsetcALTV2.c | |
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5 | funcringcsetcALTV2.u | |
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6 | funcringcsetcALTV2.f | |
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7 | funcringcsetcALTV2.g | |
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8 | eqid | |
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9 | eqid | |
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10 | eqid | |
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11 | eqid | |
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12 | eqid | |
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13 | eqid | |
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14 | 1 | ringccat | |
15 | 5 14 | syl | |
16 | 2 | setccat | |
17 | 5 16 | syl | |
18 | 1 2 3 4 5 6 | funcringcsetcALTV2lem3 | |
19 | 1 2 3 4 5 6 7 | funcringcsetcALTV2lem4 | |
20 | 1 2 3 4 5 6 7 | funcringcsetcALTV2lem8 | |
21 | 1 2 3 4 5 6 7 | funcringcsetcALTV2lem7 | |
22 | 1 2 3 4 5 6 7 | funcringcsetcALTV2lem9 | |
23 | 3 4 8 9 10 11 12 13 15 17 18 19 20 21 22 | isfuncd | |