Theorem bj-nnflemea

Description: One of four lemmas for nonfreeness: antecedent expressed with existential quantifier and consequent expressed with universal quantifier. (Contributed by BJ, 12-Aug-2023) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-nnflemea	|- ( A. x ( E. y ph -> ph ) -> ( E. y A. x ph -> A. x ph ) )

Proof

Step	Hyp	Ref	Expression
1		bj-19.12	|- ( E. y A. x ph -> A. x E. y ph )
2		alim	|- ( A. x ( E. y ph -> ph ) -> ( A. x E. y ph -> A. x ph ) )
3	1 2	syl5	|- ( A. x ( E. y ph -> ph ) -> ( E. y A. x ph -> A. x ph ) )