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Metamath Proof Explorer

Theorem sb9i

Description: Commutation of quantification and substitution variables. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 5-Aug-1993) (Proof shortened by Wolf Lammen, 15-Jun-2019) (New usage is discouraged.)

Ref Expression
Assertion sb9i ⊢ ∀ x x y φ → ∀ y y x φ

Proof

Step Hyp Ref Expression
1 sb9 ⊢ ∀ x x y φ ↔ ∀ y y x φ
2 1 biimpi ⊢ ∀ x x y φ → ∀ y y x φ