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Theorem nfimd 1477
 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 1436 . . . . 5
43nfri 1412 . . . 4
5 nfnf1 1436 . . . . 5
65nfri 1412 . . . 4
7 nfr 1411 . . . . . 6
87imim2d 48 . . . . 5
9 19.21t 1474 . . . . . 6
109biimprd 147 . . . . 5
118, 10syl9r 67 . . . 4
124, 6, 11alrimdh 1368 . . 3
13 df-nf 1350 . . 3
1412, 13syl6ibr 151 . 2
151, 2, 14sylc 56 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241  wnf 1349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  nfbid  1480  dvelimALT  1886  dvelimfv  1887  dvelimor  1894  nfmod  1917  nfraldxy  2356  cbvrald  9927
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