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Theorem nfbid 1854
 Description: If in a context is not free in and , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 29-Dec-2017.)
Hypotheses
Ref Expression
nfbid.1
nfbid.2
Assertion
Ref Expression
nfbid

Proof of Theorem nfbid
StepHypRef Expression
1 dfbi2 610 . 2
2 nfbid.1 . . . 4
3 nfbid.2 . . . 4
42, 3nfimd 1827 . . 3
53, 2nfimd 1827 . . 3
64, 5nfand 1843 . 2
71, 6nfxfrd 1580 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553 This theorem is referenced by:  nfbi  1856  nfeud2  2292  nfeqd  2585  nfiotad  5413  iota2df  5434  axextnd  8458  axrepndlem1  8459  axrepndlem2  8460  axacndlem4  8477  axacndlem5  8478  axacnd  8479  axextdist  25419 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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