Metamath Proof Explorer


Theorem rngo0cl

Description: A ring has an additive identity element. (Contributed by Steve Rodriguez, 9-Sep-2007) (New usage is discouraged.)

Ref Expression
Hypotheses ring0cl.1 G=1stR
ring0cl.2 X=ranG
ring0cl.3 Z=GIdG
Assertion rngo0cl RRingOpsZX

Proof

Step Hyp Ref Expression
1 ring0cl.1 G=1stR
2 ring0cl.2 X=ranG
3 ring0cl.3 Z=GIdG
4 1 rngogrpo RRingOpsGGrpOp
5 2 3 grpoidcl GGrpOpZX
6 4 5 syl RRingOpsZX