Theorem addridi 8321

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
addridi	|- ( A + 0 ) = A

Proof of Theorem addridi

Step	Hyp	Ref	Expression
1		mul.1	. 2 |- A e. CC
2		addrid 8317	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1397   e. wcel 2202  (class class class)co 6018   CCcc 8030   0cc0 8032   + caddc 8035

This theorem was proved from axioms:  ax-mp 5  ax-0id 8140

This theorem is referenced by:  1p0e1  9259  9p1e10  9613  num0u  9621  numnncl2  9633  decrmanc  9667  decaddi  9670  decaddci  9671  decmul1  9674  decmulnc  9677  fsumrelem  12037  demoivreALT  12340  decsplit0  13005  sinhalfpilem  15521  efipi  15531