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 2158 | . . 3 | |
2 | 1 | rgen 2510 | . 2 |
3 | mpteq12 4050 | . 2 | |
4 | 2, 3 | mpan2 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 wral 2435 cmpt 4028 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-ral 2440 df-opab 4029 df-mpt 4030 |
This theorem is referenced by: mpteq1d 4052 fmptap 5660 mpompt 5916 mpomptsx 6148 mpompts 6149 tposf12 6219 restco 12670 cnmpt1t 12781 cnmpt2t 12789 |
Copyright terms: Public domain | W3C validator |