Theorem nfth 1834

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1817 changed. (Revised by Wolf Lammen, 12-Sep-2021.)

Hypothesis

Ref	Expression
nfth.1	⊢ 𝜑

Assertion

Ref	Expression
nfth	⊢ Ⅎ𝑥𝜑

Proof of Theorem nfth

Step	Hyp	Ref	Expression
1		nftht 1825	. 2 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)
2		nfth.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1830	1 ⊢ Ⅎ𝑥𝜑

This proof depends on syntax axioms:  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828

This proof depends on definitions:  df-bi 210  df-nf 1817

This theorem is used by:  nftru  1837  nfequid  2046  iunxdif3  5063  infcvgaux1i  15934  exnel  36329  ellimcabssub0  46391