Theorem addid1i 8099

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 8095	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1353   e. wcel 2148  (class class class)co 5875   CCcc 7809   0cc0 7811   + caddc 7814

This theorem was proved from axioms:  ax-mp 5  ax-0id 7919

This theorem is referenced by:  1p0e1  9035  9p1e10  9386  num0u  9394  numnncl2  9406  decrmanc  9440  decaddi  9443  decaddci  9444  decmul1  9447  decmulnc  9450  fsumrelem  11479  demoivreALT  11781  sinhalfpilem  14215  efipi  14225