Metamath Proof Explorer


Theorem lidl1

Description: Every ring contains a unit ideal. (Contributed by Stefan O'Rear, 3-Jan-2015) (Proof shortened by AV, 18-Apr-2025)

Ref Expression
Hypotheses rnglidl0.u U = LIdeal R
rnglidl1.b B = Base R
Assertion lidl1 R Ring B U

Proof

Step Hyp Ref Expression
1 rnglidl0.u U = LIdeal R
2 rnglidl1.b B = Base R
3 ringrng R Ring R Rng
4 1 2 rnglidl1 R Rng B U
5 3 4 syl R Ring B U