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Theorem nfbid 1567
 Description: If in a context is not free in and , then 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 385 . 2
2 nfbid.1 . . . 4
3 nfbid.2 . . . 4
42, 3nfimd 1564 . . 3
53, 2nfimd 1564 . . 3
64, 5nfand 1547 . 2
71, 6nfxfrd 1451 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wnf 1436 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-gen 1425  ax-4 1487  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  nfbi  1568  nfeudv  2012  nfeqd  2294  nfiotadw  5086  iota2df  5107  bdsepnft  13074  strcollnft  13171
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