Metamath Proof Explorer


Theorem ringccatALTV

Description: The category of rings is a category. (Contributed by AV, 14-Feb-2020) (New usage is discouraged.)

Ref Expression
Hypothesis ringccatALTV.c 𝐶 = ( RingCatALTV ‘ 𝑈 )
Assertion ringccatALTV ( 𝑈𝑉𝐶 ∈ Cat )

Proof

Step Hyp Ref Expression
1 ringccatALTV.c 𝐶 = ( RingCatALTV ‘ 𝑈 )
2 eqid ( Base ‘ 𝐶 ) = ( Base ‘ 𝐶 )
3 1 2 ringccatidALTV ( 𝑈𝑉 → ( 𝐶 ∈ Cat ∧ ( Id ‘ 𝐶 ) = ( 𝑥 ∈ ( Base ‘ 𝐶 ) ↦ ( I ↾ ( Base ‘ 𝑥 ) ) ) ) )
4 3 simpld ( 𝑈𝑉𝐶 ∈ Cat )