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Mirrors > Home > QLE Home > Th. List > wfh2 | Unicode version |
Description: Weak structural analog of Foulis-Holland Theorem. |
Ref | Expression |
---|---|
wfh.1 | |
wfh.2 |
Ref | Expression |
---|---|
wfh2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wledi 405 | . . 3 | |
2 | oran 87 | . . . . . . . . . . . 12 | |
3 | 2 | bi1 118 | . . . . . . . . . . 11 |
4 | df-a 40 | . . . . . . . . . . . . . . 15 | |
5 | 4 | bi1 118 | . . . . . . . . . . . . . 14 |
6 | 5 | wcon2 208 | . . . . . . . . . . . . 13 |
7 | 6 | wran 369 | . . . . . . . . . . . 12 |
8 | 7 | wr4 199 | . . . . . . . . . . 11 |
9 | 3, 8 | wr2 371 | . . . . . . . . . 10 |
10 | 9 | wcon2 208 | . . . . . . . . 9 |
11 | 10 | wlan 370 | . . . . . . . 8 |
12 | an4 86 | . . . . . . . . . 10 | |
13 | 12 | bi1 118 | . . . . . . . . 9 |
14 | wfh.1 | . . . . . . . . . . . . . 14 | |
15 | 14 | wcomcom 414 | . . . . . . . . . . . . 13 |
16 | 15 | wcomcom2 415 | . . . . . . . . . . . 12 |
17 | 16 | wcom3ii 419 | . . . . . . . . . . 11 |
18 | ancom 74 | . . . . . . . . . . . 12 | |
19 | 18 | bi1 118 | . . . . . . . . . . 11 |
20 | 17, 19 | wr2 371 | . . . . . . . . . 10 |
21 | 20 | wran 369 | . . . . . . . . 9 |
22 | 13, 21 | wr2 371 | . . . . . . . 8 |
23 | 11, 22 | wr2 371 | . . . . . . 7 |
24 | an4 86 | . . . . . . . 8 | |
25 | 24 | bi1 118 | . . . . . . 7 |
26 | 23, 25 | wr2 371 | . . . . . 6 |
27 | ax-a1 30 | . . . . . . . . . . 11 | |
28 | 27 | bi1 118 | . . . . . . . . . 10 |
29 | 28 | wr5-2v 366 | . . . . . . . . 9 |
30 | 29 | wlan 370 | . . . . . . . 8 |
31 | wfh.2 | . . . . . . . . . 10 | |
32 | 31 | wcomcom3 416 | . . . . . . . . 9 |
33 | 32 | wcom3ii 419 | . . . . . . . 8 |
34 | 30, 33 | wr2 371 | . . . . . . 7 |
35 | 34 | wran 369 | . . . . . 6 |
36 | 26, 35 | wr2 371 | . . . . 5 |
37 | anass 76 | . . . . . 6 | |
38 | 37 | bi1 118 | . . . . 5 |
39 | 36, 38 | wr2 371 | . . . 4 |
40 | anass 76 | . . . . . . . . 9 | |
41 | 40 | bi1 118 | . . . . . . . 8 |
42 | 41 | wr1 197 | . . . . . . 7 |
43 | an12 81 | . . . . . . . 8 | |
44 | 43 | bi1 118 | . . . . . . 7 |
45 | dff 101 | . . . . . . . 8 | |
46 | 45 | bi1 118 | . . . . . . 7 |
47 | 42, 44, 46 | w3tr1 374 | . . . . . 6 |
48 | 47 | wlan 370 | . . . . 5 |
49 | an0 108 | . . . . . 6 | |
50 | 49 | bi1 118 | . . . . 5 |
51 | 48, 50 | wr2 371 | . . . 4 |
52 | 39, 51 | wr2 371 | . . 3 |
53 | 1, 52 | wom5 381 | . 2 |
54 | 53 | wr1 197 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 tb 5 wo 6 wa 7 wt 8 wf 9 wcmtr 29 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a4 33 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 ax-wom 361 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-i2 45 df-le 129 df-le1 130 df-le2 131 df-cmtr 134 |
This theorem is referenced by: wfh4 426 |
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