Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 7672. Proofs should normally use addcl 7745 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 7618 | . . . 4 | |
3 | 1, 2 | wcel 1480 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1480 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | caddc 7623 | . . . 4 | |
8 | 1, 4, 7 | co 5774 | . . 3 |
9 | 8, 2 | wcel 1480 | . 2 |
10 | 6, 9 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: addcl 7745 |
Copyright terms: Public domain | W3C validator |