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Mirrors > Home > ILE Home > Th. List > nfbid | 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, 29-Dec-2017.) |
Ref | Expression |
---|---|
nfbid.1 | |
nfbid.2 |
Ref | Expression |
---|---|
nfbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi2 380 | . 2 | |
2 | nfbid.1 | . . . 4 | |
3 | nfbid.2 | . . . 4 | |
4 | 2, 3 | nfimd 1517 | . . 3 |
5 | 3, 2 | nfimd 1517 | . . 3 |
6 | 4, 5 | nfand 1500 | . 2 |
7 | 1, 6 | nfxfrd 1404 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wnf 1389 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-4 1440 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: nfbi 1521 nfeudv 1956 nfeqd 2233 nfiotadxy 4890 iota2df 4911 bdsepnft 10678 strcollnft 10779 |
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