Theorem nfth 1727

Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1710 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 1718	. 2 ⊢ (∀𝑥𝜑 → Ⅎ𝑥𝜑)
2		nfth.1	. 2 ⊢ 𝜑
3	1, 2	mpg 1724	1 ⊢ Ⅎ𝑥𝜑

Syntax hints:  Ⅎwnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722

This theorem depends on definitions:  df-bi 197  df-nf 1710

This theorem is referenced by:  nftru  1730  nfequid  1940  exanOLDOLD  2169  sbc2ie  3505  iunxdif3  4606  infcvgaux1i  14589  exnel  31708  elrnmpt1sf  39376  ellimcabssub0  39849