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Mirrors > Home > NFE 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 609 | . 2 | |
2 | nfbid.1 | . . . 4 | |
3 | nfbid.2 | . . . 4 | |
4 | 2, 3 | nfimd 1808 | . . 3 |
5 | 3, 2 | nfimd 1808 | . . 3 |
6 | 4, 5 | nfand 1822 | . 2 |
7 | 1, 6 | nfxfrd 1571 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wnf 1544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 |
This theorem is referenced by: nfbi 1834 nfeud2 2216 nfeqd 2503 nfiotad 4342 iota2df 4365 |
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