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Mirrors > Home > ILE Home > Th. List > nfexd | Unicode version |
Description: If is not free in , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 7-Feb-2018.) |
Ref | Expression |
---|---|
nfald.1 | |
nfald.2 |
Ref | Expression |
---|---|
nfexd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfald.1 | . . . . . . 7 | |
2 | 1 | nfri 1412 | . . . . . 6 |
3 | nfald.2 | . . . . . . 7 | |
4 | df-nf 1350 | . . . . . . 7 | |
5 | 3, 4 | sylib 127 | . . . . . 6 |
6 | 2, 5 | alrimih 1358 | . . . . 5 |
7 | alcom 1367 | . . . . 5 | |
8 | 6, 7 | sylib 127 | . . . 4 |
9 | exim 1490 | . . . . 5 | |
10 | 9 | alimi 1344 | . . . 4 |
11 | 8, 10 | syl 14 | . . 3 |
12 | 19.12 1555 | . . . . 5 | |
13 | 12 | imim2i 12 | . . . 4 |
14 | 13 | alimi 1344 | . . 3 |
15 | 11, 14 | syl 14 | . 2 |
16 | df-nf 1350 | . 2 | |
17 | 15, 16 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wnf 1349 wex 1381 |
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-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: nfsbxy 1818 nfsbxyt 1819 nfeudv 1915 nfmod 1917 nfeld 2193 nfrexdxy 2357 |
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