Theorem addridi 8411

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
addridi	⊢ (𝐴 + 0) = 𝐴

Proof of Theorem addridi

Step	Hyp	Ref	Expression
1		mul.1	. 2 ⊢ 𝐴 ∈ ℂ
2		addrid 8407	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1398   ∈ wcel 2203  (class class class)co 6049  ℂcc 8121  0cc0 8123   + caddc 8126

This theorem was proved from axioms:  ax-mp 5  ax-0id 8231

This theorem is referenced by:  1p0e1  9349  9p1e10  9707  num0u  9715  numnncl2  9727  decrmanc  9761  decaddi  9764  decaddci  9765  decmul1  9768  decmulnc  9771  fsumrelem  12150  demoivreALT  12453  decsplit0  13118  sinhalfpilem  15643  efipi  15653