Theorem addid1i 8040

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 e. CC

Assertion

Ref	Expression
addid1i	|- ( A + 0 ) = A

Proof of Theorem addid1i

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		addid1 8036	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1343   e. wcel 2136  (class class class)co 5842   CCcc 7751   0cc0 7753   + caddc 7756

This theorem was proved from axioms:  ax-mp 5  ax-0id 7861

This theorem is referenced by:  1p0e1  8973  9p1e10  9324  num0u  9332  numnncl2  9344  decrmanc  9378  decaddi  9381  decaddci  9382  decmul1  9385  decmulnc  9388  fsumrelem  11412  demoivreALT  11714  sinhalfpilem  13352  efipi  13362