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Theorem nfexd 1734
 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
nfald.2
Assertion
Ref Expression
nfexd

Proof of Theorem nfexd
StepHypRef Expression
1 nfald.1 . . . . . . 7
21nfri 1499 . . . . . 6
3 nfald.2 . . . . . . 7
4 df-nf 1437 . . . . . . 7
53, 4sylib 121 . . . . . 6
62, 5alrimih 1445 . . . . 5
7 alcom 1454 . . . . 5
86, 7sylib 121 . . . 4
9 exim 1578 . . . . 5
109alimi 1431 . . . 4
118, 10syl 14 . . 3
12 19.12 1643 . . . . 5
1312imim2i 12 . . . 4
1413alimi 1431 . . 3
1511, 14syl 14 . 2
16 df-nf 1437 . 2
1715, 16sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329  wnf 1436  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  nfsbxy  1915  nfsbxyt  1916  nfeudv  2014  nfmod  2016  nfeld  2297  nfrexdxy  2468
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