Theorem addid1i 7250

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 7246	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 7	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1284   ∈ wcel 1433  (class class class)co 5532  ℂcc 6979  0cc0 6981   + caddc 6984

This theorem was proved from axioms:  ax-mp 7  ax-0id 7084

This theorem is referenced by:  1p0e1  8154  9p1e10  8479  num0u  8487  numnncl2  8499  decrmanc  8533  decaddi  8536  decaddci  8537  decmul1  8540  decmulnc  8543