Description: The zero (additive identity) of a non-unital ring is an element of each two-sided ideal of the ring which is a subgroup of the ring. (Contributed by AV, 20-Feb-2025)
Ref | Expression | ||
---|---|---|---|
Hypotheses | rng2idlsubgsubrng.r | ||
rng2idlsubgsubrng.i | |||
rng2idlsubgsubrng.u | |||
Assertion | rng2idlsubg0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rng2idlsubgsubrng.r | ||
2 | rng2idlsubgsubrng.i | ||
3 | rng2idlsubgsubrng.u | ||
4 | 1 2 3 | rng2idlsubgsubrng | |
5 | subrngsubg | ||
6 | eqid | ||
7 | 6 | subg0cl | |
8 | 4 5 7 | 3syl |