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Mirrors > Home > QLE Home > Th. List > orbi | Unicode version |
Description: Disjunction of biconditionals. |
Ref | Expression |
---|---|
orbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfb 94 | . . 3 | |
2 | dfb 94 | . . 3 | |
3 | 1, 2 | 2or 72 | . 2 |
4 | ax-a2 31 | . 2 | |
5 | ax-a3 32 | . . 3 | |
6 | ancom 74 | . . . . . . . 8 | |
7 | 6 | lor 70 | . . . . . . 7 |
8 | imp3 841 | . . . . . . . 8 | |
9 | 8 | ax-r1 35 | . . . . . . 7 |
10 | 7, 9 | ax-r2 36 | . . . . . 6 |
11 | 10 | ax-r5 38 | . . . . 5 |
12 | ax-a3 32 | . . . . 5 | |
13 | df-i1 44 | . . . . . . . 8 | |
14 | lear 161 | . . . . . . . . . . 11 | |
15 | leo 158 | . . . . . . . . . . 11 | |
16 | 14, 15 | letr 137 | . . . . . . . . . 10 |
17 | 16 | lecom 180 | . . . . . . . . 9 |
18 | 17 | comcom 453 | . . . . . . . 8 |
19 | 13, 18 | bctr 181 | . . . . . . 7 |
20 | comi12 707 | . . . . . . 7 | |
21 | 19, 20 | fh4rc 482 | . . . . . 6 |
22 | 13 | ax-r5 38 | . . . . . . . 8 |
23 | ax-a2 31 | . . . . . . . 8 | |
24 | 16 | df-le2 131 | . . . . . . . 8 |
25 | 22, 23, 24 | 3tr 65 | . . . . . . 7 |
26 | 25 | lan 77 | . . . . . 6 |
27 | 21, 26 | ax-r2 36 | . . . . 5 |
28 | 11, 12, 27 | 3tr2 64 | . . . 4 |
29 | 28 | lor 70 | . . 3 |
30 | df-i2 45 | . . . . . . . 8 | |
31 | 30 | ax-r5 38 | . . . . . . 7 |
32 | ax-a3 32 | . . . . . . 7 | |
33 | 31, 32 | ax-r2 36 | . . . . . 6 |
34 | lear 161 | . . . . . . . . 9 | |
35 | leo 158 | . . . . . . . . 9 | |
36 | 34, 35 | letr 137 | . . . . . . . 8 |
37 | 36 | lecom 180 | . . . . . . 7 |
38 | 37 | comcom 453 | . . . . . 6 |
39 | 33, 38 | bctr 181 | . . . . 5 |
40 | lea 160 | . . . . . . . . . . 11 | |
41 | 40, 35 | letr 137 | . . . . . . . . . 10 |
42 | 41 | lecom 180 | . . . . . . . . 9 |
43 | 42 | comcom 453 | . . . . . . . 8 |
44 | anor1 88 | . . . . . . . 8 | |
45 | 43, 44 | cbtr 182 | . . . . . . 7 |
46 | 45 | comcom7 460 | . . . . . 6 |
47 | 33, 46 | bctr 181 | . . . . 5 |
48 | 39, 47 | fh4 472 | . . . 4 |
49 | 30 | lor 70 | . . . . . . . 8 |
50 | leo 158 | . . . . . . . . . 10 | |
51 | 34, 50 | letr 137 | . . . . . . . . 9 |
52 | 51 | df-le2 131 | . . . . . . . 8 |
53 | 49, 52 | ax-r2 36 | . . . . . . 7 |
54 | 53 | ax-r5 38 | . . . . . 6 |
55 | ax-a3 32 | . . . . . 6 | |
56 | ax-a2 31 | . . . . . . . 8 | |
57 | orordi 112 | . . . . . . . 8 | |
58 | df-i2 45 | . . . . . . . . 9 | |
59 | 58, 30 | 2or 72 | . . . . . . . 8 |
60 | 56, 57, 59 | 3tr1 63 | . . . . . . 7 |
61 | 32, 60 | ax-r2 36 | . . . . . 6 |
62 | 54, 55, 61 | 3tr2 64 | . . . . 5 |
63 | or12 80 | . . . . . 6 | |
64 | ax-a2 31 | . . . . . . 7 | |
65 | orordi 112 | . . . . . . 7 | |
66 | df-i1 44 | . . . . . . . . 9 | |
67 | ancom 74 | . . . . . . . . . 10 | |
68 | 67 | lor 70 | . . . . . . . . 9 |
69 | 66, 68 | ax-r2 36 | . . . . . . . 8 |
70 | 13, 69 | 2or 72 | . . . . . . 7 |
71 | 64, 65, 70 | 3tr1 63 | . . . . . 6 |
72 | 63, 71 | ax-r2 36 | . . . . 5 |
73 | 62, 72 | 2an 79 | . . . 4 |
74 | 48, 73 | ax-r2 36 | . . 3 |
75 | 5, 29, 74 | 3tr 65 | . 2 |
76 | 3, 4, 75 | 3tr 65 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 tb 5 wo 6 wa 7 wi1 12 wi2 13 |
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-r3 439 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-i2 45 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: orbile 843 |
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