Metamath Proof Explorer


Theorem bj-nnfth

Description: A variable is nonfree in a theorem, inference form. (Contributed by BJ, 28-Jul-2023)

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

Proof

Step Hyp Ref Expression
1 bj-nnfth.1 φ
2 bj-nnftht φ x φ Ⅎ' x φ
3 1 2 bj-mpgs Ⅎ' x φ