Metamath Proof Explorer

Theorem bj-axc4

Description: Over minimal calculus, the modal axiom (4) ( hba1 ) and the modal axiom (K) ( ax-4 ) together imply axc4 . (Contributed by BJ, 29-Nov-2020) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion bj-axc4 ⊢ ∀ x φ → ∀ x ∀ x φ → ∀ x ∀ x φ → ψ → ∀ x ∀ x φ → ∀ x ψ → ∀ x ∀ x φ → ψ → ∀ x φ → ∀ x ψ

Proof

Step Hyp Ref Expression
1 bj-imim21 ⊢ ∀ x φ → ∀ x ∀ x φ → ∀ x ∀ x φ → ψ → ∀ x ∀ x φ → ∀ x ψ → ∀ x ∀ x φ → ψ → ∀ x φ → ∀ x ψ