Theorem nfnth 1458

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 641	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3	2	nfi 1455	1 ⊢ Ⅎ𝑥𝜑

Syntax hints:  ¬ wn 3  ∀wal 1346  Ⅎwnf 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-gen 1442

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by: (None)