Theorem addridi 8185

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 8181	. 2 ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ (𝐴 + 0) = 𝐴

Syntax hints:   = wceq 1364   ∈ wcel 2167  (class class class)co 5925  ℂcc 7894  0cc0 7896   + caddc 7899

This theorem was proved from axioms:  ax-mp 5  ax-0id 8004

This theorem is referenced by:  1p0e1  9123  9p1e10  9476  num0u  9484  numnncl2  9496  decrmanc  9530  decaddi  9533  decaddci  9534  decmul1  9537  decmulnc  9540  fsumrelem  11653  demoivreALT  11956  decsplit0  12621  sinhalfpilem  15111  efipi  15121