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Theorem nfnf 1466
Description: If is not free in , it is not free in  F/. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.)
Hypothesis
Ref Expression
nfal.1  F/
Assertion
Ref Expression
nfnf  F/ F/

Proof of Theorem nfnf
StepHypRef Expression
1 df-nf 1347 . 2  F/
2 nfal.1 . . . 4  F/
32nfal 1465 . . . 4  F/
42, 3nfim 1461 . . 3  F/
54nfal 1465 . 2  F/
61, 5nfxfr 1360 1  F/ F/
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   F/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-5 1333  ax-7 1334  ax-gen 1335  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  nfnfc  2181
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