Description: The zero element of a ring belongs to its base set. (Contributed by Mario Carneiro, 12-Jan-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ring0cl.b | |
|
ring0cl.z | |
||
Assertion | ring0cl | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ring0cl.b | |
|
2 | ring0cl.z | |
|
3 | ringgrp | |
|
4 | 1 2 | grpidcl | |
5 | 3 4 | syl | |