Metamath Proof Explorer


Theorem subidd

Description: Subtraction of a number from itself. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis negidd.1 ⊢ φ → A ∈ ℂ
Assertion subidd ⊢ φ → A − A = 0

Proof

Step Hyp Ref Expression
1 negidd.1 ⊢ φ → A ∈ ℂ
2 subid ⊢ A ∈ ℂ → A − A = 0
3 1 2 syl ⊢ φ → A − A = 0