Metamath Proof Explorer


Theorem assraddsubd

Description: Associate RHS addition-subtraction. (Contributed by David A. Wheeler, 15-Oct-2018)

Ref Expression
Hypotheses assraddsubd.1 ⊢ φ → B ∈ ℂ
assraddsubd.2 ⊢ φ → C ∈ ℂ
assraddsubd.3 ⊢ φ → D ∈ ℂ
assraddsubd.4 ⊢ φ → A = B + C - D
Assertion assraddsubd ⊢ φ → A = B + C - D

Proof

Step Hyp Ref Expression
1 assraddsubd.1 ⊢ φ → B ∈ ℂ
2 assraddsubd.2 ⊢ φ → C ∈ ℂ
3 assraddsubd.3 ⊢ φ → D ∈ ℂ
4 assraddsubd.4 ⊢ φ → A = B + C - D
5 1 2 3 addsubassd ⊢ φ → B + C - D = B + C - D
6 4 5 eqtrd ⊢ φ → A = B + C - D