This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem dividi

Description: A number divided by itself is one. (Contributed by NM, 9-Feb-1995)

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

Proof

Step Hyp Ref Expression
1 divclz.1 ⊢ A ∈ ℂ
2 reccl.2 ⊢ A ≠ 0
3 divid ⊢ A ∈ ℂ ∧ A ≠ 0 → A A = 1
4 1 2 3 mp2an ⊢ A A = 1