Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dmoprab | Unicode version |
Description: The domain of an operation class abstraction. (Contributed by NM, 17-Mar-1995.) (Revised by David Abernethy, 19-Jun-2012.) |
Ref | Expression |
---|---|
dmoprab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfoprab2 5811 | . . 3 | |
2 | 1 | dmeqi 4735 | . 2 |
3 | dmopab 4745 | . 2 | |
4 | exrot3 1668 | . . . . 5 | |
5 | 19.42v 1878 | . . . . . 6 | |
6 | 5 | 2exbii 1585 | . . . . 5 |
7 | 4, 6 | bitri 183 | . . . 4 |
8 | 7 | abbii 2253 | . . 3 |
9 | df-opab 3985 | . . 3 | |
10 | 8, 9 | eqtr4i 2161 | . 2 |
11 | 2, 3, 10 | 3eqtri 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wex 1468 cab 2123 cop 3525 copab 3983 cdm 4534 coprab 5768 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-dm 4544 df-oprab 5771 |
This theorem is referenced by: dmoprabss 5846 reldmoprab 5849 fnoprabg 5865 dmaddpq 7180 dmmulpq 7181 |
Copyright terms: Public domain | W3C validator |