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Theorem nfnf 1949
Description: If is not free in , it is not free in . (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.)
Hypothesis
Ref Expression
nfal.1
Assertion
Ref Expression
nfnf

Proof of Theorem nfnf
StepHypRef Expression
1 df-nf 1617 . 2
2 nfal.1 . . . 4
32nfal 1947 . . . 4
42, 3nfim 1920 . . 3
54nfal 1947 . 2
61, 5nfxfr 1645 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  F/wnf 1616
This theorem is referenced by:  nfnfc  2628  nfnfcALT  2629  bj-nfnfc  34429  bj-nfcf  34492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617
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