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Theorem nfth 1369
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 1368 . 2 (𝜑 → ∀𝑥𝜑)
32nfi 1367 1 𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nftru  1371  nfequid  1606  sbt  1683  sbc2ie  2857
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