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Mirrors > Home > ILE Home > Th. List > ax-addcl | Unicode version |
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddcl 7894. Proofs should normally use addcl 7967 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-addcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cc 7840 |
. . . 4
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3 | 1, 2 | wcel 2160 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 2160 |
. . 3
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6 | 3, 5 | wa 104 |
. 2
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7 | caddc 7845 |
. . . 4
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8 | 1, 4, 7 | co 5897 |
. . 3
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9 | 8, 2 | wcel 2160 |
. 2
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10 | 6, 9 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: addcl 7967 |
Copyright terms: Public domain | W3C validator |