Description: The cofinality of any set is an ordinal (although it only makes sense when A is an ordinal). (Contributed by Mario Carneiro, 9-Mar-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | cfon | ⊢ ( cf ‘ 𝐴 ) ∈ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cardcf | ⊢ ( card ‘ ( cf ‘ 𝐴 ) ) = ( cf ‘ 𝐴 ) | |
2 | cardon | ⊢ ( card ‘ ( cf ‘ 𝐴 ) ) ∈ On | |
3 | 1 2 | eqeltrri | ⊢ ( cf ‘ 𝐴 ) ∈ On |