Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mpteq1 | Unicode version |
Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2171 | . . 3 | |
2 | 1 | rgen 2523 | . 2 |
3 | mpteq12 4072 | . 2 | |
4 | 2, 3 | mpan2 423 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 wral 2448 cmpt 4050 |
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-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-ral 2453 df-opab 4051 df-mpt 4052 |
This theorem is referenced by: mpteq1d 4074 fmptap 5686 mpompt 5945 mpomptsx 6176 mpompts 6177 tposf12 6248 restco 12968 cnmpt1t 13079 cnmpt2t 13087 |
Copyright terms: Public domain | W3C validator |