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Mirrors > Home > ILE Home > Th. List > mulcomi | GIF version |
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.) |
Ref | Expression |
---|---|
axi.1 | ⊢ 𝐴 ∈ ℂ |
axi.2 | ⊢ 𝐵 ∈ ℂ |
Ref | Expression |
---|---|
mulcomi | ⊢ (𝐴 · 𝐵) = (𝐵 · 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.1 | . 2 ⊢ 𝐴 ∈ ℂ | |
2 | axi.2 | . 2 ⊢ 𝐵 ∈ ℂ | |
3 | mulcom 7749 | . 2 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) = (𝐵 · 𝐴)) | |
4 | 1, 2, 3 | mp2an 422 | 1 ⊢ (𝐴 · 𝐵) = (𝐵 · 𝐴) |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ∈ wcel 1480 (class class class)co 5774 ℂcc 7618 · cmul 7625 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 ax-mulcom 7721 |
This theorem is referenced by: mulcomli 7773 8th4div3 8939 numma2c 9227 nummul2c 9231 9t11e99 9311 binom2i 10401 fac3 10478 tanval2ap 11420 sincosq4sgn 12910 |
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