Metamath Proof Explorer


Theorem subcli

Description: Closure law for subtraction. (Contributed by NM, 26-Nov-1994) (Revised by Mario Carneiro, 21-Dec-2013)

Ref Expression
Hypotheses negidi.1 𝐴 ∈ ℂ
pncan3i.2 𝐵 ∈ ℂ
Assertion subcli ( 𝐴𝐵 ) ∈ ℂ

Proof

Step Hyp Ref Expression
1 negidi.1 𝐴 ∈ ℂ
2 pncan3i.2 𝐵 ∈ ℂ
3 subcl ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( 𝐴𝐵 ) ∈ ℂ )
4 1 2 3 mp2an ( 𝐴𝐵 ) ∈ ℂ