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Theorem nfth 1398
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 1397 . 2 (𝜑 → ∀𝑥𝜑)
32nfi 1396 1 𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1383
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  nftru  1400  nfequid  1635  sbt  1714  sbc2ie  2910  omsinds  4435
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