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Metamath Proof Explorer

Theorem pncan3i

Description: Subtraction and addition of equals. (Contributed by NM, 26-Nov-1994)

Ref Expression
Hypotheses negidi.1 ⊢ A ∈ ℂ
pncan3i.2 ⊢ B ∈ ℂ
Assertion pncan3i ⊢ A + B - A = B

Proof

Step Hyp Ref Expression
1 negidi.1 ⊢ A ∈ ℂ
2 pncan3i.2 ⊢ B ∈ ℂ
3 pncan3 ⊢ A ∈ ℂ ∧ B ∈ ℂ → A + B - A = B
4 1 2 3 mp2an ⊢ A + B - A = B