Theorem addid1i 8093

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 8089	. 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 5870  ℂcc 7804  0cc0 7806   + caddc 7809

This theorem was proved from axioms:  ax-mp 5  ax-0id 7914

This theorem is referenced by:  1p0e1  9029  9p1e10  9380  num0u  9388  numnncl2  9400  decrmanc  9434  decaddi  9437  decaddci  9438  decmul1  9441  decmulnc  9444  fsumrelem  11470  demoivreALT  11772  sinhalfpilem  13994  efipi  14004