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Mirrors > Home > HOLE Home > Th. List > dfan2 | Unicode version |
Description: An alternative defintion of the "and" term in terms of the context conjunction. |
Ref | Expression |
---|---|
dfan2.1 | |
dfan2.2 |
Ref | Expression |
---|---|
dfan2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wan 126 | . . . . . 6 | |
2 | dfan2.1 | . . . . . 6 | |
3 | dfan2.2 | . . . . . 6 | |
4 | 1, 2, 3 | wov 64 | . . . . 5 |
5 | 4 | trud 27 | . . . 4 |
6 | wv 58 | . . . . . . . 8 | |
7 | 6, 2, 3 | wov 64 | . . . . . . 7 |
8 | 7 | wl 59 | . . . . . 6 |
9 | wv 58 | . . . . . . . 8 | |
10 | 9 | wl 59 | . . . . . . 7 |
11 | 10 | wl 59 | . . . . . 6 |
12 | 8, 11 | wc 45 | . . . . 5 |
13 | 4 | id 25 | . . . . . . 7 |
14 | 2, 3 | anval 138 | . . . . . . . 8 |
15 | 4, 14 | a1i 28 | . . . . . . 7 |
16 | 13, 15 | mpbi 72 | . . . . . 6 |
17 | 8, 11, 16 | ceq1 79 | . . . . 5 |
18 | 6, 11 | weqi 68 | . . . . . . . . . 10 |
19 | 18 | id 25 | . . . . . . . . 9 |
20 | 6, 2, 3, 19 | oveq 92 | . . . . . . . 8 |
21 | 9, 2 | weqi 68 | . . . . . . . . . . 11 |
22 | 21 | id 25 | . . . . . . . . . 10 |
23 | wv 58 | . . . . . . . . . . . 12 | |
24 | 23, 3 | weqi 68 | . . . . . . . . . . 11 |
25 | 24, 2 | eqid 73 | . . . . . . . . . 10 |
26 | 9, 2, 3, 22, 25 | ovl 107 | . . . . . . . . 9 |
27 | 18, 26 | a1i 28 | . . . . . . . 8 |
28 | 7, 20, 27 | eqtri 85 | . . . . . . 7 |
29 | 7, 11, 28 | cl 106 | . . . . . 6 |
30 | 4, 29 | a1i 28 | . . . . 5 |
31 | wtru 40 | . . . . . . . 8 | |
32 | 6, 31, 31 | wov 64 | . . . . . . 7 |
33 | 6, 31, 31, 19 | oveq 92 | . . . . . . . 8 |
34 | 9, 31 | weqi 68 | . . . . . . . . . . 11 |
35 | 34 | id 25 | . . . . . . . . . 10 |
36 | 23, 31 | weqi 68 | . . . . . . . . . . 11 |
37 | 36, 31 | eqid 73 | . . . . . . . . . 10 |
38 | 9, 31, 31, 35, 37 | ovl 107 | . . . . . . . . 9 |
39 | 18, 38 | a1i 28 | . . . . . . . 8 |
40 | 32, 33, 39 | eqtri 85 | . . . . . . 7 |
41 | 32, 11, 40 | cl 106 | . . . . . 6 |
42 | 4, 41 | a1i 28 | . . . . 5 |
43 | 12, 17, 30, 42 | 3eqtr3i 87 | . . . 4 |
44 | 5, 43 | mpbir 77 | . . 3 |
45 | 23 | wl 59 | . . . . . . 7 |
46 | 45 | wl 59 | . . . . . 6 |
47 | 8, 46 | wc 45 | . . . . 5 |
48 | 8, 46, 16 | ceq1 79 | . . . . 5 |
49 | 6, 46 | weqi 68 | . . . . . . . . . 10 |
50 | 49 | id 25 | . . . . . . . . 9 |
51 | 6, 2, 3, 50 | oveq 92 | . . . . . . . 8 |
52 | 7, 46, 51 | cl 106 | . . . . . . 7 |
53 | 21, 23 | eqid 73 | . . . . . . . . 9 |
54 | 24 | id 25 | . . . . . . . . 9 |
55 | 23, 2, 3, 53, 54 | ovl 107 | . . . . . . . 8 |
56 | 31, 55 | a1i 28 | . . . . . . 7 |
57 | 47, 52, 56 | eqtri 85 | . . . . . 6 |
58 | 4, 57 | a1i 28 | . . . . 5 |
59 | 6, 31, 31, 50 | oveq 92 | . . . . . . . 8 |
60 | 34, 23 | eqid 73 | . . . . . . . . . 10 |
61 | 36 | id 25 | . . . . . . . . . 10 |
62 | 23, 31, 31, 60, 61 | ovl 107 | . . . . . . . . 9 |
63 | 49, 62 | a1i 28 | . . . . . . . 8 |
64 | 32, 59, 63 | eqtri 85 | . . . . . . 7 |
65 | 32, 46, 64 | cl 106 | . . . . . 6 |
66 | 4, 65 | a1i 28 | . . . . 5 |
67 | 47, 48, 58, 66 | 3eqtr3i 87 | . . . 4 |
68 | 5, 67 | mpbir 77 | . . 3 |
69 | 44, 68 | jca 18 | . 2 |
70 | 2, 3 | simpl 22 | . . . . . . 7 |
71 | 70 | eqtru 76 | . . . . . 6 |
72 | 2, 3 | simpr 23 | . . . . . . 7 |
73 | 72 | eqtru 76 | . . . . . 6 |
74 | 6, 31, 31, 71, 73 | oveq12 90 | . . . . 5 |
75 | 32, 74 | eqcomi 70 | . . . 4 |
76 | 7, 75 | leq 81 | . . 3 |
77 | 70 | ax-cb1 29 | . . . 4 |
78 | 77, 14 | a1i 28 | . . 3 |
79 | 76, 78 | mpbir 77 | . 2 |
80 | 69, 79 | dedi 75 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tan 109 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-an 118 |
This theorem is referenced by: hbct 145 mpd 146 ex 148 |
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