Theorem addid1i 7155

Description: 0 is an additive identity. (Contributed by NM, 23-Nov-1994.) (Revised by Scott Fenton, 3-Jan-2013.)

Hypothesis

Ref	Expression
mul.1	⊢ 𝐴 ∈ ℂ

Assertion

Ref	Expression
addid1i	⊢ (𝐴 + 0) = 𝐴

Proof of Theorem addid1i

Step	Hyp	Ref	Expression
1		mul.1	. 2 ⊢ 𝐴 ∈ ℂ
2		addid1 7151	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 7	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1243   ∈ wcel 1393  (class class class)co 5512  ℂcc 6887  0cc0 6889   + caddc 6892

This theorem was proved from axioms:  ax-mp 7  ax-0id 6992

This theorem is referenced by:  1p0e1  8032  num0u  8376  numnncl2  8384  dec10  8397  decaddi  8411  decaddci  8412