Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfbid | 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, 29-Dec-2017.) |
Ref | Expression |
---|---|
nfbid.1 | |
nfbid.2 |
Ref | Expression |
---|---|
nfbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi2 386 | . 2 | |
2 | nfbid.1 | . . . 4 | |
3 | nfbid.2 | . . . 4 | |
4 | 2, 3 | nfimd 1578 | . . 3 |
5 | 3, 2 | nfimd 1578 | . . 3 |
6 | 4, 5 | nfand 1561 | . 2 |
7 | 1, 6 | nfxfrd 1468 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 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: nfbi 1582 nfeudv 2034 nfeqd 2327 nfiotadw 5161 iota2df 5182 bdsepnft 13882 |
Copyright terms: Public domain | W3C validator |