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Theorem nfnth 1370
Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.)
Hypothesis
Ref Expression
nfnth.1 ¬ 𝜑
Assertion
Ref Expression
nfnth 𝑥𝜑

Proof of Theorem nfnth
StepHypRef Expression
1 nfnth.1 . . 3 ¬ 𝜑
21pm2.21i 585 . 2 (𝜑 → ∀𝑥𝜑)
32nfi 1367 1 𝑥𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wal 1257  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-in2 555  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by: (None)
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