Metamath Proof Explorer


Theorem int-add02d

Description: Second AdditionZero generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

Ref Expression
Hypotheses int-add02d.1 ⊢ φ → A ∈ ℝ
int-add02d.2 ⊢ φ → A = B
Assertion int-add02d ⊢ φ → 0 + A = B

Proof

Step Hyp Ref Expression
1 int-add02d.1 ⊢ φ → A ∈ ℝ
2 int-add02d.2 ⊢ φ → A = B
3 1 recnd ⊢ φ → A ∈ ℂ
4 3 addlidd ⊢ φ → 0 + A = A
5 4 2 eqtrd ⊢ φ → 0 + A = B