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	$$⊢\aleph \left(A\right)\prec \left({\aleph \left(A\right)}^{\mathrm{cf}\left(\aleph \left(A\right)\right)}\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\left(y\in \mathrm{cf}\left(\aleph \left(A\right)\right)⟼\mathrm{har}\left(f\left(y\right)\right)\right)=\left(y\in \mathrm{cf}\left(\aleph \left(A\right)\right)⟼\mathrm{har}\left(f\left(y\right)\right)\right)$$
2	1	pwcfsdom	$$⊢\aleph \left(A\right)\prec \left({\aleph \left(A\right)}^{\mathrm{cf}\left(\aleph \left(A\right)\right)}\right)$$