Theorem addid1i 8061

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 8057	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1348   e. wcel 2141  (class class class)co 5853   CCcc 7772   0cc0 7774   + caddc 7777

This theorem was proved from axioms:  ax-mp 5  ax-0id 7882

This theorem is referenced by:  1p0e1  8994  9p1e10  9345  num0u  9353  numnncl2  9365  decrmanc  9399  decaddi  9402  decaddci  9403  decmul1  9406  decmulnc  9409  fsumrelem  11434  demoivreALT  11736  sinhalfpilem  13506  efipi  13516