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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 4856 | . 2 | |
2 | rnmpt.1 | . . . 4 | |
3 | df-mpt 4050 | . . . 4 | |
4 | 2, 3 | eqtri 2191 | . . 3 |
5 | 4 | rneqi 4837 | . 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 4047 cmpt 4048 crn 4610 |
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 4105 ax-pow 4158 ax-pr 4192 |
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 3566 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-mpt 4050 df-cnv 4617 df-dm 4619 df-rn 4620 |
This theorem is referenced by: elrnmpt 4858 elrnmpt1 4860 elrnmptg 4861 dfiun3g 4866 dfiin3g 4867 fnrnfv 5541 fmpt 5644 fnasrn 5672 fnasrng 5674 fliftf 5776 abrexex 6094 abrexexg 6095 fo1st 6134 fo2nd 6135 qliftf 6596 negfi 11184 restco 12933 |
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