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Theorem nfth 1718
Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1701 changed. (Revised by Wolf Lammen, 12-Sep-2021.)
Hypothesis
Ref Expression
nfth.1 𝜑
Assertion
Ref Expression
nfth 𝑥𝜑

Proof of Theorem nfth
StepHypRef Expression
1 nftht0 1709 . 2 (∀𝑥𝜑 → Ⅎ𝑥𝜑)
2 nfth.1 . 2 𝜑
31, 2mpg 1715 1 𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1699
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713
This theorem depends on definitions:  df-bi 196  df-nf 1701
This theorem is referenced by:  nftru  1721  nfequid  1927  exanOLDOLD  2155  sbc2ie  3472  iunxdif3  4542  infcvgaux1i  14428  exnel  30952  elrnmpt1sf  38371  ellimcabssub0  38684
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