Theorem nfnth 1556

Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.)

Hypothesis

Ref	Expression
nfnth.1	⊢ ¬ φ

Assertion

Ref	Expression
nfnth	⊢ Ⅎxφ

Proof of Theorem nfnth

Step	Hyp	Ref	Expression
1		nfnth.1	. . 3 ⊢ ¬ φ
2	1	pm2.21i 123	. 2 ⊢ (φ → ∀xφ)
3	2	nfi 1551	1 ⊢ Ⅎxφ

Syntax hints:  ¬ wn 3  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546

This theorem depends on definitions:  df-bi 177  df-nf 1545

This theorem is referenced by: (None)