Theorem nfth 1457

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
hbth.1	⊢ 𝜑

Assertion

Ref	Expression
nfth	⊢ Ⅎ𝑥𝜑

Proof of Theorem nfth

Step	Hyp	Ref	Expression
1		hbth.1	. . 3 ⊢ 𝜑
2	1	hbth 1456	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3	2	nfi 1455	1 ⊢ Ⅎ𝑥𝜑

Syntax hints:  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-gen 1442

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

This theorem is referenced by:  nftru  1459  nfequid  1695  sbt  1777  sbc2ie  3026  omsinds  4606