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Mirrors > Home > ILE Home > Th. List > ax-mulrcl | Unicode version |
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7668. Proofs should normally use remulcl 7741 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulrcl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cr 7612 | . . . 4 | |
3 | 1, 2 | wcel 1480 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1480 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | cmul 7618 | . . . 4 | |
8 | 1, 4, 7 | co 5767 | . . 3 |
9 | 8, 2 | wcel 1480 | . 2 |
10 | 6, 9 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: remulcl 7741 |
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