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Mirrors > Home > ILE Home > Th. List > ax-mulcl | Unicode version |
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7798. Proofs should normally use mulcl 7871 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulcl |
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 | cmul 7749 | . . . 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: mulcl 7871 |
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