![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > mpoeq123i | Unicode version |
Description: An equality inference for the maps-to notation. (Contributed by NM, 15-Jul-2013.) |
Ref | Expression |
---|---|
mpoeq123i.1 |
![]() ![]() ![]() ![]() |
mpoeq123i.2 |
![]() ![]() ![]() ![]() |
mpoeq123i.3 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
mpoeq123i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpoeq123i.1 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | 1 | a1i 9 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | mpoeq123i.2 |
. . . 4
![]() ![]() ![]() ![]() | |
4 | 3 | a1i 9 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | mpoeq123i.3 |
. . . 4
![]() ![]() ![]() ![]() | |
6 | 5 | a1i 9 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 2, 4, 6 | mpoeq123dv 5950 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 7 | mptru 1372 |
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-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-11 1516 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-oprab 5892 df-mpo 5893 |
This theorem is referenced by: ofmres 6150 |
Copyright terms: Public domain | W3C validator |