Theorem addridi 8221

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 8217	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1373   ∈ wcel 2177  (class class class)co 5951  ℂcc 7930  0cc0 7932   + caddc 7935

This theorem was proved from axioms:  ax-mp 5  ax-0id 8040

This theorem is referenced by:  1p0e1  9159  9p1e10  9513  num0u  9521  numnncl2  9533  decrmanc  9567  decaddi  9570  decaddci  9571  decmul1  9574  decmulnc  9577  fsumrelem  11826  demoivreALT  12129  decsplit0  12794  sinhalfpilem  15307  efipi  15317