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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 7164. Proofs should normally use addcl 7230 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 7111 |
. . . 4
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3 | 1, 2 | wcel 1434 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 1434 |
. . 3
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6 | 3, 5 | wa 102 |
. 2
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7 | caddc 7116 |
. . . 4
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8 | 1, 4, 7 | co 5564 |
. . 3
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9 | 8, 2 | wcel 1434 |
. 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 7230 |
Copyright terms: Public domain | W3C validator |