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Metamath Proof Explorer

Theorem sqmuli

Description: Distribution of squaring over multiplication. (Contributed by NM, 3-Sep-1999)

Ref Expression
Hypotheses sqval.1 ⊢ A ∈ ℂ
sqmul.2 ⊢ B ∈ ℂ
Assertion sqmuli ⊢ A ⁢ B 2 = A 2 ⁢ B 2

Proof

Step Hyp Ref Expression
1 sqval.1 ⊢ A ∈ ℂ
2 sqmul.2 ⊢ B ∈ ℂ
3 sqmul ⊢ A ∈ ℂ ∧ B ∈ ℂ → A ⁢ B 2 = A 2 ⁢ B 2
4 1 2 3 mp2an ⊢ A ⁢ B 2 = A 2 ⁢ B 2