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Theorem nfbid 1774
 Description: If is not free in and , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
nfnd.1
nfimd.2
Assertion
Ref Expression
nfbid

Proof of Theorem nfbid
StepHypRef Expression
1 dfbi1 184 . 2
2 nfnd.1 . . . . 5
3 nfimd.2 . . . . 5
42, 3nfimd 1773 . . . 4
53, 2nfimd 1773 . . . . 5
65nfnd 1772 . . . 4
74, 6nfimd 1773 . . 3
87nfnd 1772 . 2
91, 8nfxfrd 1561 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176  wnf 1534 This theorem is referenced by:  nfeud2  2168  nfeqd  2446  nfiotad  5238  iota2df  5259  axextnd  8229  axrepndlem1  8230  axrepndlem2  8231  axacndlem4  8248  axacndlem5  8249  axacnd  8250  axextdist  24227 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1535
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