Theorem addridi 8314

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 8310	. 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 6013  ℂcc 8023  0cc0 8025   + caddc 8028

This theorem was proved from axioms:  ax-mp 5  ax-0id 8133

This theorem is referenced by:  1p0e1  9252  9p1e10  9606  num0u  9614  numnncl2  9626  decrmanc  9660  decaddi  9663  decaddci  9664  decmul1  9667  decmulnc  9670  fsumrelem  12025  demoivreALT  12328  decsplit0  12993  sinhalfpilem  15508  efipi  15518