Metamath Proof Explorer


Theorem 2txmxeqx

Description: Two times a complex number minus the number itself results in the number itself. (Contributed by Alexander van der Vekens, 8-Jun-2018)

Ref Expression
Assertion 2txmxeqx ( 𝑋 ∈ ℂ → ( ( 2 · 𝑋 ) − 𝑋 ) = 𝑋 )

Proof

Step Hyp Ref Expression
1 id ⊢ ( 𝑋 ∈ ℂ → 𝑋 ∈ ℂ )
2 2times ⊢ ( 𝑋 ∈ ℂ → ( 2 · 𝑋 ) = ( 𝑋 + 𝑋 ) )
3 1 1 2 mvrladdd ⊢ ( 𝑋 ∈ ℂ → ( ( 2 · 𝑋 ) − 𝑋 ) = 𝑋 )