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Theorem nfimd 1474
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  F/
nfimd.2  F/
Assertion
Ref Expression
nfimd  F/

Proof of Theorem nfimd
StepHypRef Expression
1 nfimd.1 . 2  F/
2 nfimd.2 . 2  F/
3 nfnf1 1433 . . . . 5  F/ F/
43nfri 1409 . . . 4  F/  F/
5 nfnf1 1433 . . . . 5  F/ F/
65nfri 1409 . . . 4  F/  F/
7 nfr 1408 . . . . . 6  F/
87imim2d 48 . . . . 5  F/
9 19.21t 1471 . . . . . 6  F/
109biimprd 147 . . . . 5  F/
118, 10syl9r 67 . . . 4  F/  F/
124, 6, 11alrimdh 1365 . . 3  F/  F/
13 df-nf 1347 . . 3  F/
1412, 13syl6ibr 151 . 2  F/  F/  F/
151, 2, 14sylc 56 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   F/wnf 1346
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 1333  ax-gen 1335  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  nfbid  1477  dvelimALT  1883  dvelimfv  1884  dvelimor  1891  nfmod  1914  nfraldxy  2350  cbvrald  9242
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