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Mirrors > Home > ILE Home > Th. List > dvelimfv | Unicode version |
Description: Like dvelimf 1968 but with a distinct variable constraint on and . (Contributed by Jim Kingdon, 6-Mar-2018.) |
Ref | Expression |
---|---|
dvelimfv.1 | |
dvelimfv.2 | |
dvelimfv.3 |
Ref | Expression |
---|---|
dvelimfv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnae 1685 | . . . 4 | |
2 | ax-i12 1470 | . . . . . . . . 9 | |
3 | orcom 702 | . . . . . . . . . 10 | |
4 | 3 | orbi2i 736 | . . . . . . . . 9 |
5 | 2, 4 | mpbi 144 | . . . . . . . 8 |
6 | orass 741 | . . . . . . . 8 | |
7 | 5, 6 | mpbir 145 | . . . . . . 7 |
8 | nfae 1682 | . . . . . . . . . . 11 | |
9 | ax16ALT 1815 | . . . . . . . . . . 11 | |
10 | 8, 9 | nfd 1488 | . . . . . . . . . 10 |
11 | dvelimfv.1 | . . . . . . . . . . . 12 | |
12 | 11 | nfi 1423 | . . . . . . . . . . 11 |
13 | 12 | a1i 9 | . . . . . . . . . 10 |
14 | 10, 13 | nfimd 1549 | . . . . . . . . 9 |
15 | df-nf 1422 | . . . . . . . . . 10 | |
16 | id 19 | . . . . . . . . . . 11 | |
17 | 12 | a1i 9 | . . . . . . . . . . 11 |
18 | 16, 17 | nfimd 1549 | . . . . . . . . . 10 |
19 | 15, 18 | sylbir 134 | . . . . . . . . 9 |
20 | 14, 19 | jaoi 690 | . . . . . . . 8 |
21 | 20 | orim1i 734 | . . . . . . 7 |
22 | 7, 21 | ax-mp 5 | . . . . . 6 |
23 | orcom 702 | . . . . . 6 | |
24 | 22, 23 | mpbi 144 | . . . . 5 |
25 | 24 | ori 697 | . . . 4 |
26 | 1, 25 | nfald 1718 | . . 3 |
27 | dvelimfv.2 | . . . . 5 | |
28 | dvelimfv.3 | . . . . 5 | |
29 | 27, 28 | equsalh 1689 | . . . 4 |
30 | 29 | nfbii 1434 | . . 3 |
31 | 26, 30 | sylib 121 | . 2 |
32 | 31 | nfrd 1485 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 682 wal 1314 wnf 1421 |
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-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 |
This theorem is referenced by: (None) |
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