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