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Metamath Proof Explorer

Theorem recidi

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 9-Feb-1995)

Ref Expression
Hypotheses divclz.1 ⊢ A ∈ ℂ
reccl.2 ⊢ A ≠ 0
Assertion recidi ⊢ A ⁢ 1 A = 1

Proof

Step Hyp Ref Expression
1 divclz.1 ⊢ A ∈ ℂ
2 reccl.2 ⊢ A ≠ 0
3 1 recidzi ⊢ A ≠ 0 → A ⁢ 1 A = 1
4 2 3 ax-mp ⊢ A ⁢ 1 A = 1