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Theorem nfnth 1543
Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.)
Hypothesis
Ref Expression
nfnth.1  |-  -.  ph
Assertion
Ref Expression
nfnth  |-  F/ x ph

Proof of Theorem nfnth
StepHypRef Expression
1 nfnth.1 . . 3  |-  -.  ph
21pm2.21i 123 . 2  |-  ( ph  ->  A. x ph )
32nfi 1538 1  |-  F/ x ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1527   F/wnf 1531
This theorem is referenced by:  nd1  8209  nd2  8210
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533
This theorem depends on definitions:  df-bi 177  df-nf 1532
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