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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 7796. Proofs should normally use addcl 7869 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 7742 | . . . 4 | |
3 | 1, 2 | wcel 2135 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 2135 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | caddc 7747 | . . . 4 | |
8 | 1, 4, 7 | co 5836 | . . 3 |
9 | 8, 2 | wcel 2135 | . 2 |
10 | 6, 9 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: addcl 7869 |
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