Metamath Proof Explorer


Theorem bj-nnfbii

Description: If two formulas are equivalent for all x , then nonfreeness of x in one of them is equivalent to nonfreeness in the other, inference form. See bj-nnfbi . (Contributed by BJ, 18-Nov-2023)

Ref Expression
Hypothesis bj-nnfbii.1 φ ψ
Assertion bj-nnfbii Ⅎ' x φ Ⅎ' x ψ

Proof

Step Hyp Ref Expression
1 bj-nnfbii.1 φ ψ
2 bj-nnfbi φ ψ x φ ψ Ⅎ' x φ Ⅎ' x ψ
3 1 2 bj-mpgs Ⅎ' x φ Ⅎ' x ψ