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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 7833. Proofs should normally use mulcom 7903 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulcom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cc 7772 | . . . 4 | |
3 | 1, 2 | wcel 2141 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 2141 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | cmul 7779 | . . . 4 | |
8 | 1, 4, 7 | co 5853 | . . 3 |
9 | 4, 1, 7 | co 5853 | . . 3 |
10 | 8, 9 | wceq 1348 | . 2 |
11 | 6, 10 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: mulcom 7903 |
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