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Theorem nfnth 1445
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 636 . 2 (𝜑 → ∀𝑥𝜑)
32nfi 1442 1 𝑥𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wal 1333  wnf 1440
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-in2 605  ax-gen 1429
This theorem depends on definitions:  df-bi 116  df-nf 1441
This theorem is referenced by: (None)
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