Theorem addid1i 8099

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 8095	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1353   ∈ wcel 2148  (class class class)co 5875  ℂcc 7809  0cc0 7811   + caddc 7814

This theorem was proved from axioms:  ax-mp 5  ax-0id 7919

This theorem is referenced by:  1p0e1  9035  9p1e10  9386  num0u  9394  numnncl2  9406  decrmanc  9440  decaddi  9443  decaddci  9444  decmul1  9447  decmulnc  9450  fsumrelem  11479  demoivreALT  11781  sinhalfpilem  14215  efipi  14225