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Theorem nfth 1440
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 𝑥𝜑

Proof of Theorem nfth
StepHypRef Expression
1 hbth.1 . . 3 𝜑
21hbth 1439 . 2 (𝜑 → ∀𝑥𝜑)
32nfi 1438 1 𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1425
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  nftru  1442  nfequid  1678  sbt  1757  sbc2ie  2975  omsinds  4530
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