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Theorem nfexd 1641
Description: If is not free in , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 7-Feb-2018.)
Hypotheses
Ref Expression
nfald.1  F/
nfald.2  F/
Assertion
Ref Expression
nfexd  F/

Proof of Theorem nfexd
StepHypRef Expression
1 nfald.1 . . . . . . 7  F/
21nfri 1409 . . . . . 6
3 nfald.2 . . . . . . 7  F/
4 df-nf 1347 . . . . . . 7  F/
53, 4sylib 127 . . . . . 6
62, 5alrimih 1355 . . . . 5
7 alcom 1364 . . . . 5
86, 7sylib 127 . . . 4
9 exim 1487 . . . . 5
109alimi 1341 . . . 4
118, 10syl 14 . . 3
12 19.12 1552 . . . . 5
1312imim2i 12 . . . 4
1413alimi 1341 . . 3
1511, 14syl 14 . 2
16 df-nf 1347 . 2  F/
1715, 16sylibr 137 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   F/wnf 1346  wex 1378
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-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  nfsbxy  1815  nfsbxyt  1816  nfeudv  1912  nfmod  1914  nfeld  2190  nfrexdxy  2351
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