Theorem nfth 1350

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 1349	. 2 ⊢ (φ → ∀xφ)
3	2	nfi 1348	1 ⊢ Ⅎxφ

Syntax hints:  Ⅎwnf 1346

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  nftru  1352  nfequid  1587  sbt  1664  sbc2ie  2823