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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 7640. Proofs should normally use addcl 7713 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cc 7586 | . . . 4 | |
3 | 1, 2 | wcel 1465 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1465 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | caddc 7591 | . . . 4 | |
8 | 1, 4, 7 | co 5742 | . . 3 |
9 | 8, 2 | wcel 1465 | . 2 |
10 | 6, 9 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: addcl 7713 |
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