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Theorem nfnth 1629
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 131 . 2  |-  ( ph  ->  A. x ph )
32nfi 1624 1  |-  F/ x ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   A.wal 1393   F/wnf 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619
This theorem depends on definitions:  df-bi 185  df-nf 1618
This theorem is referenced by:  nffal  1630  nd1  8979  nd2  8980
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