Theorem addridi 8326

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 8322	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1397   ∈ wcel 2201  (class class class)co 6023  ℂcc 8035  0cc0 8037   + caddc 8040

This theorem was proved from axioms:  ax-mp 5  ax-0id 8145

This theorem is referenced by:  1p0e1  9264  9p1e10  9618  num0u  9626  numnncl2  9638  decrmanc  9672  decaddi  9675  decaddci  9676  decmul1  9679  decmulnc  9682  fsumrelem  12055  demoivreALT  12358  decsplit0  13023  sinhalfpilem  15544  efipi  15554