Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dfrn2 | Unicode version |
Description: Alternate definition of range. Definition 4 of [Suppes] p. 60. (Contributed by NM, 27-Dec-1996.) |
Ref | Expression |
---|---|
dfrn2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn 4597 | . 2 | |
2 | df-dm 4596 | . 2 | |
3 | vex 2715 | . . . . 5 | |
4 | vex 2715 | . . . . 5 | |
5 | 3, 4 | brcnv 4769 | . . . 4 |
6 | 5 | exbii 1585 | . . 3 |
7 | 6 | abbii 2273 | . 2 |
8 | 1, 2, 7 | 3eqtri 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wex 1472 cab 2143 class class class wbr 3965 ccnv 4585 cdm 4586 crn 4587 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-cnv 4594 df-dm 4596 df-rn 4597 |
This theorem is referenced by: dfrn3 4775 dfdm4 4778 dm0rn0 4803 dmmrnm 4805 dfrnf 4827 dfima2 4930 funcnv3 5232 |
Copyright terms: Public domain | W3C validator |