Theorem addridi 8414

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 8410	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1398   e. wcel 2203  (class class class)co 6049   CCcc 8124   0cc0 8126   + caddc 8129

This theorem was proved from axioms:  ax-mp 5  ax-0id 8234

This theorem is referenced by:  1p0e1  9352  9p1e10  9710  num0u  9718  numnncl2  9730  decrmanc  9764  decaddi  9767  decaddci  9768  decmul1  9771  decmulnc  9774  fsumrelem  12153  demoivreALT  12456  decsplit0  13121  sinhalfpilem  15648  efipi  15658