Metamath Proof Explorer


Theorem subidd

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

Ref Expression
Hypothesis negidd.1 ( 𝜑𝐴 ∈ ℂ )
Assertion subidd ( 𝜑 → ( 𝐴𝐴 ) = 0 )

Proof

Step Hyp Ref Expression
1 negidd.1 ( 𝜑𝐴 ∈ ℂ )
2 subid ( 𝐴 ∈ ℂ → ( 𝐴𝐴 ) = 0 )
3 1 2 syl ( 𝜑 → ( 𝐴𝐴 ) = 0 )