Theorem nfth 1553

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 1552	. 2 ⊢ (φ → ∀xφ)
3	2	nfi 1551	1 ⊢ Ⅎxφ

Syntax hints:  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:  nftru  1554  nfequid  1678  sbt  2033  sbc2ie  3113