Theorem addid1i 7897

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 7893	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1331   e. wcel 1480  (class class class)co 5767   CCcc 7611   0cc0 7613   + caddc 7616

This theorem was proved from axioms:  ax-mp 5  ax-0id 7721

This theorem is referenced by:  1p0e1  8829  9p1e10  9177  num0u  9185  numnncl2  9197  decrmanc  9231  decaddi  9234  decaddci  9235  decmul1  9238  decmulnc  9241  fsumrelem  11233  demoivreALT  11469  sinhalfpilem  12861  efipi  12871