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Metamath Proof Explorer

Theorem mvrladdd

Description: Move the left term in a sum on the RHS to the LHS, deduction form. (Contributed by David A. Wheeler, 11-Oct-2018)

Ref Expression
Hypotheses mvrraddd.1 ⊢ φ → B ∈ ℂ
mvrraddd.2 ⊢ φ → C ∈ ℂ
mvrraddd.3 ⊢ φ → A = B + C
Assertion mvrladdd ⊢ φ → A − B = C

Proof

Step Hyp Ref Expression
1 mvrraddd.1 ⊢ φ → B ∈ ℂ
2 mvrraddd.2 ⊢ φ → C ∈ ℂ
3 mvrraddd.3 ⊢ φ → A = B + C
4 1 2 3 comraddd ⊢ φ → A = C + B
5 2 1 4 mvrraddd ⊢ φ → A − B = C