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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 7599. Proofs should normally use addcl 7669 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 7545 |
. . . 4
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3 | 1, 2 | wcel 1463 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 1463 |
. . 3
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6 | 3, 5 | wa 103 |
. 2
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7 | caddc 7550 |
. . . 4
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8 | 1, 4, 7 | co 5728 |
. . 3
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9 | 8, 2 | wcel 1463 |
. 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 7669 |
Copyright terms: Public domain | W3C validator |