Metamath Proof Explorer
Description: The zero of a unital ring is a right-absorbing element. (Contributed by FL, 31-Aug-2009) (Proof shortened by AV, 30-Mar-2025)
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Ref |
Expression |
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Hypotheses |
ringz.b |
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|
ringz.t |
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|
ringz.z |
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Assertion |
ringrz |
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Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ringz.b |
|
2 |
|
ringz.t |
|
3 |
|
ringz.z |
|
4 |
|
ringrng |
|
5 |
1 2 3
|
rngrz |
|
6 |
4 5
|
sylan |
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