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Theorem nfnth 1351
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 574 . 2 (φxφ)
32nfi 1348 1 xφ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wal 1240  wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-gen 1335
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by: (None)
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