Theorem addridi 8299

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 8295	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1395   ∈ wcel 2200  (class class class)co 6007  ℂcc 8008  0cc0 8010   + caddc 8013

This theorem was proved from axioms:  ax-mp 5  ax-0id 8118

This theorem is referenced by:  1p0e1  9237  9p1e10  9591  num0u  9599  numnncl2  9611  decrmanc  9645  decaddi  9648  decaddci  9649  decmul1  9652  decmulnc  9655  fsumrelem  11998  demoivreALT  12301  decsplit0  12966  sinhalfpilem  15481  efipi  15491