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Theorem nfimd 1808
 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, 30-Dec-2017.)
Hypotheses
Ref Expression
nfimd.1
nfimd.2
Assertion
Ref Expression
nfimd

Proof of Theorem nfimd
StepHypRef Expression
1 nfimd.1 . 2
2 nfimd.2 . 2
3 nfnf1 1790 . . . 4
4 nfnf1 1790 . . . 4
5 nfr 1761 . . . . . 6
65imim2d 48 . . . . 5
7 19.21t 1795 . . . . . 6
87biimprd 214 . . . . 5
96, 8syl9r 67 . . . 4
103, 4, 9alrimd 1769 . . 3
11 df-nf 1545 . . 3
1210, 11syl6ibr 218 . 2
131, 2, 12sylc 56 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1540  wnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ex 1542  df-nf 1545 This theorem is referenced by:  nfimOLD  1814  hbimd  1815  19.23tOLD  1819  nfand  1822  nfbid  1832  nfbidOLD  1833  nfnfOLD  1846  19.21tOLD  1863  dvelimf  1997  nfsb4t  2080  nfmod2  2217  nfrald  2665  nfifd  3685
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