Theorem bj-nnflemee

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

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

Proof

Step	Hyp	Ref	Expression
1		excom	|- ( E. y E. x ph <-> E. x E. y ph )
2		exim	|- ( A. x ( E. y ph -> ph ) -> ( E. x E. y ph -> E. x ph ) )
3	1 2	syl5bi	|- ( A. x ( E. y ph -> ph ) -> ( E. y E. x ph -> E. x ph ) )