Theorem bj-pwcfsdom

Description: Remove hypothesis from pwcfsdom . Illustration of how to remove a "proof-facilitating hypothesis". (Can use it to shorten theorems using pwcfsdom .) (Contributed by BJ, 14-Sep-2019)

	Ref	Expression
Assertion	bj-pwcfsdom	⊢ ( ℵ ‘ 𝐴 ) ≺ ( ( ℵ ‘ 𝐴 ) ↑m ( cf ‘ ( ℵ ‘ 𝐴 ) ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( 𝑦 ∈ ( cf ‘ ( ℵ ‘ 𝐴 ) ) ↦ ( har ‘ ( 𝑓 ‘ 𝑦 ) ) ) = ( 𝑦 ∈ ( cf ‘ ( ℵ ‘ 𝐴 ) ) ↦ ( har ‘ ( 𝑓 ‘ 𝑦 ) ) )
2	1	pwcfsdom	⊢ ( ℵ ‘ 𝐴 ) ≺ ( ( ℵ ‘ 𝐴 ) ↑m ( cf ‘ ( ℵ ‘ 𝐴 ) ) )