Description: Distribution of negative over subtraction. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negsubdi3d.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
negsubdi3d.2 | ⊢ ( 𝜑 → 𝐵 ∈ ℂ ) | ||
Assertion | negsubdi3d | ⊢ ( 𝜑 → - ( 𝐴 − 𝐵 ) = ( - 𝐴 − - 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negsubdi3d.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
2 | negsubdi3d.2 | ⊢ ( 𝜑 → 𝐵 ∈ ℂ ) | |
3 | 1 2 | negsubdi2d | ⊢ ( 𝜑 → - ( 𝐴 − 𝐵 ) = ( 𝐵 − 𝐴 ) ) |
4 | 1 2 | neg2subd | ⊢ ( 𝜑 → ( - 𝐴 − - 𝐵 ) = ( 𝐵 − 𝐴 ) ) |
5 | 3 4 | eqtr4d | ⊢ ( 𝜑 → - ( 𝐴 − 𝐵 ) = ( - 𝐴 − - 𝐵 ) ) |