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