Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dfdmf | Unicode version |
Description: Definition of domain, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
dfdmf.1 | |
dfdmf.2 |
Ref | Expression |
---|---|
dfdmf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dm 4544 | . 2 | |
2 | nfcv 2279 | . . . . 5 | |
3 | dfdmf.2 | . . . . 5 | |
4 | nfcv 2279 | . . . . 5 | |
5 | 2, 3, 4 | nfbr 3969 | . . . 4 |
6 | nfv 1508 | . . . 4 | |
7 | breq2 3928 | . . . 4 | |
8 | 5, 6, 7 | cbvex 1729 | . . 3 |
9 | 8 | abbii 2253 | . 2 |
10 | nfcv 2279 | . . . . 5 | |
11 | dfdmf.1 | . . . . 5 | |
12 | nfcv 2279 | . . . . 5 | |
13 | 10, 11, 12 | nfbr 3969 | . . . 4 |
14 | 13 | nfex 1616 | . . 3 |
15 | nfv 1508 | . . 3 | |
16 | breq1 3927 | . . . 4 | |
17 | 16 | exbidv 1797 | . . 3 |
18 | 14, 15, 17 | cbvab 2261 | . 2 |
19 | 1, 9, 18 | 3eqtri 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wex 1468 cab 2123 wnfc 2266 class class class wbr 3924 cdm 4534 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-dm 4544 |
This theorem is referenced by: dmopab 4745 |
Copyright terms: Public domain | W3C validator |