Metamath Proof Explorer


Theorem rngo0rid

Description: The additive identity of a ring is a right 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 rngo0rid RRingOpsAXAGZ=A

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 grporid GGrpOpAXAGZ=A
6 4 5 sylan RRingOpsAXAGZ=A