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Mirrors > Home > ILE Home > Th. List > ax-mulcom | Unicode version |
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7647. Proofs should normally use mulcom 7717 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulcom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cc 7586 | . . . 4 | |
3 | 1, 2 | wcel 1465 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1465 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | cmul 7593 | . . . 4 | |
8 | 1, 4, 7 | co 5742 | . . 3 |
9 | 4, 1, 7 | co 5742 | . . 3 |
10 | 8, 9 | wceq 1316 | . 2 |
11 | 6, 10 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: mulcom 7717 |
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