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Mirrors > Home > ILE Home > Th. List > nfimd | Unicode version |
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, 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 1537 | . . . . 5 | |
4 | 3 | nfri 1512 | . . . 4 |
5 | nfnf1 1537 | . . . . 5 | |
6 | 5 | nfri 1512 | . . . 4 |
7 | nfr 1511 | . . . . . 6 | |
8 | 7 | imim2d 54 | . . . . 5 |
9 | 19.21t 1575 | . . . . . 6 | |
10 | 9 | biimprd 157 | . . . . 5 |
11 | 8, 10 | syl9r 73 | . . . 4 |
12 | 4, 6, 11 | alrimdh 1472 | . . 3 |
13 | df-nf 1454 | . . 3 | |
14 | 12, 13 | syl6ibr 161 | . 2 |
15 | 1, 2, 14 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1346 wnf 1453 |
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 1440 ax-gen 1442 ax-4 1503 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-nf 1454 |
This theorem is referenced by: nfbid 1581 dvelimALT 2003 dvelimfv 2004 dvelimor 2011 nfmod 2036 nfraldw 2502 nfraldxy 2503 nfixpxy 6693 cbvrald 13788 |
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