Metamath Proof Explorer

Theorem 19.27v

Description: Version of 19.27 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 3-Jun-2004)

Ref Expression
Assertion 19.27v ⊢ ∀ x φ ∧ ψ ↔ ∀ x φ ∧ ψ

Proof

Step Hyp Ref Expression
1 19.26 ⊢ ∀ x φ ∧ ψ ↔ ∀ x φ ∧ ∀ x ψ
2 19.3v ⊢ ∀ x ψ ↔ ψ
3 2 anbi2i ⊢ ∀ x φ ∧ ∀ x ψ ↔ ∀ x φ ∧ ψ
4 1 3 bitri ⊢ ∀ x φ ∧ ψ ↔ ∀ x φ ∧ ψ