Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rnmpt | Unicode version |
Description: The range of a function in maps-to notation. (Contributed by Scott Fenton, 21-Mar-2011.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
rnmpt.1 |
Ref | Expression |
---|---|
rnmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rnopab 4858 | . 2 | |
2 | rnmpt.1 | . . . 4 | |
3 | df-mpt 4052 | . . . 4 | |
4 | 2, 3 | eqtri 2191 | . . 3 |
5 | 4 | rneqi 4839 | . 2 |
6 | df-rex 2454 | . . 3 | |
7 | 6 | abbii 2286 | . 2 |
8 | 1, 5, 7 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 cab 2156 wrex 2449 copab 4049 cmpt 4050 crn 4612 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-mpt 4052 df-cnv 4619 df-dm 4621 df-rn 4622 |
This theorem is referenced by: elrnmpt 4860 elrnmpt1 4862 elrnmptg 4863 dfiun3g 4868 dfiin3g 4869 fnrnfv 5543 fmpt 5646 fnasrn 5674 fnasrng 5676 fliftf 5778 abrexex 6096 abrexexg 6097 fo1st 6136 fo2nd 6137 qliftf 6598 negfi 11191 restco 12968 |
Copyright terms: Public domain | W3C validator |