Theorem addridi 8296

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 8292	. 2 |- ( A e. CC -> ( A + 0 ) = A )
3	1, 2	ax-mp 5	1 |- ( A + 0 ) = A

Syntax hints:   = wceq 1395   e. wcel 2200  (class class class)co 6007   CCcc 8005   0cc0 8007   + caddc 8010

This theorem was proved from axioms:  ax-mp 5  ax-0id 8115

This theorem is referenced by:  1p0e1  9234  9p1e10  9588  num0u  9596  numnncl2  9608  decrmanc  9642  decaddi  9645  decaddci  9646  decmul1  9649  decmulnc  9652  fsumrelem  11992  demoivreALT  12295  decsplit0  12960  sinhalfpilem  15475  efipi  15485