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Mirrors > Home > ILE Home > Th. List > nfimd | Unicode version |
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.) |
Ref | Expression |
---|---|
nfimd.1 | |
nfimd.2 |
Ref | Expression |
---|---|
nfimd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfimd.1 | . 2 | |
2 | nfimd.2 | . 2 | |
3 | nfnf1 1436 | . . . . 5 | |
4 | 3 | nfri 1412 | . . . 4 |
5 | nfnf1 1436 | . . . . 5 | |
6 | 5 | nfri 1412 | . . . 4 |
7 | nfr 1411 | . . . . . 6 | |
8 | 7 | imim2d 48 | . . . . 5 |
9 | 19.21t 1474 | . . . . . 6 | |
10 | 9 | biimprd 147 | . . . . 5 |
11 | 8, 10 | syl9r 67 | . . . 4 |
12 | 4, 6, 11 | alrimdh 1368 | . . 3 |
13 | df-nf 1350 | . . 3 | |
14 | 12, 13 | syl6ibr 151 | . 2 |
15 | 1, 2, 14 | sylc 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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