Theorem addridi 8420

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 8416	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1398   ∈ wcel 2205  (class class class)co 6052  ℂcc 8130  0cc0 8132   + caddc 8135

This theorem was proved from axioms:  ax-mp 5  ax-0id 8240

This theorem is referenced by:  1p0e1  9358  9p1e10  9717  num0u  9725  numnncl2  9737  decrmanc  9771  decaddi  9774  decaddci  9775  decmul1  9778  decmulnc  9781  fsumrelem  12165  demoivreALT  12468  decsplit0  13133  sinhalfpilem  15705  efipi  15715