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Theorem nfbid 1496
 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 374 . 2
2 nfbid.1 . . . 4
3 nfbid.2 . . . 4
42, 3nfimd 1493 . . 3
53, 2nfimd 1493 . . 3
64, 5nfand 1476 . 2
71, 6nfxfrd 1380 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wnf 1365 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366 This theorem is referenced by:  nfbi  1497  nfeudv  1931  nfeqd  2208  nfiotadxy  4898  iota2df  4919  bdsepnft  10394  strcollnft  10496
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