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 5898 | . 2 |
8 | 7 | mptru 1351 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wtru 1343 cmpo 5841 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-oprab 5843 df-mpo 5844 |
This theorem is referenced by: ofmres 6099 |
Copyright terms: Public domain | W3C validator |