Metamath Proof Explorer


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 x φ y φ x φ y x φ

Proof

Step Hyp Ref Expression
1 alim x φ y φ x φ x y φ
2 ax-11 x y φ y x φ
3 1 2 syl6 x φ y φ x φ y x φ