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Theorem nfbid 1832
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  F/
nfbid.2  F/
Assertion
Ref Expression
nfbid  F/

Proof of Theorem nfbid
StepHypRef Expression
1 dfbi2 609 . 2
2 nfbid.1 . . . 4  F/
3 nfbid.2 . . . 4  F/
42, 3nfimd 1808 . . 3  F/
53, 2nfimd 1808 . . 3  F/
64, 5nfand 1822 . 2  F/
71, 6nfxfrd 1571 1  F/
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358   F/wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
This theorem is referenced by:  nfbi  1834  nfeud2  2216  nfeqd  2503  nfiotad  4342  iota2df  4365
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