Theorem bj-nnflemaa

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

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

Proof

Step	Hyp	Ref	Expression
1		alim	|- ( A. x ( ph -> A. y ph ) -> ( A. x ph -> A. x A. y ph ) )
2		ax-11	|- ( A. x A. y ph -> A. y A. x ph )
3	1 2	syl6	|- ( A. x ( ph -> A. y ph ) -> ( A. x ph -> A. y A. x ph ) )