![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > dvelimdf | Unicode version |
Description: Deduction form of dvelimf 2027. This version may be useful if we want to avoid ax-17 1537 and use ax-16 1825 instead. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.) |
Ref | Expression |
---|---|
dvelimdf.1 |
![]() ![]() ![]() ![]() |
dvelimdf.2 |
![]() ![]() ![]() ![]() |
dvelimdf.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dvelimdf.4 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dvelimdf.5 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
dvelimdf |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvelimdf.2 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | dvelimdf.3 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | alrimi 1533 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | nfsb4t 2026 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | syl 14 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | dvelimdf.1 |
. . 3
![]() ![]() ![]() ![]() | |
7 | dvelimdf.4 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | dvelimdf.5 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 1, 7, 8 | sbied 1799 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 6, 9 | nfbidf 1550 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 5, 10 | sylibd 149 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 |
This theorem is referenced by: dvelimdc 2353 |
Copyright terms: Public domain | W3C validator |