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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 7674. Proofs should normally use mulcl 7747 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulcl |
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 | cmul 7625 | . . . 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: mulcl 7747 |
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