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Mirrors > Home > QLE Home > Th. List > ud1lem1 | Unicode version |
Description: Lemma for unified disjunction. |
Ref | Expression |
---|---|
ud1lem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i1 44 | . 2 | |
2 | ud1lem0c 277 | . . . 4 | |
3 | df-i1 44 | . . . . 5 | |
4 | df-i1 44 | . . . . 5 | |
5 | 3, 4 | 2an 79 | . . . 4 |
6 | 2, 5 | 2or 72 | . . 3 |
7 | ancom 74 | . . . . . . . 8 | |
8 | 7 | lor 70 | . . . . . . 7 |
9 | 8 | lan 77 | . . . . . 6 |
10 | coman1 185 | . . . . . . . . 9 | |
11 | 10 | comcom2 183 | . . . . . . . 8 |
12 | coman2 186 | . . . . . . . . 9 | |
13 | 12 | comcom2 183 | . . . . . . . 8 |
14 | 11, 13 | fh3r 475 | . . . . . . 7 |
15 | 14 | ax-r1 35 | . . . . . 6 |
16 | 9, 15 | ax-r2 36 | . . . . 5 |
17 | 16 | lor 70 | . . . 4 |
18 | or12 80 | . . . . 5 | |
19 | 10 | comcom 453 | . . . . . . . 8 |
20 | comorr 184 | . . . . . . . . . 10 | |
21 | 20 | comcom2 183 | . . . . . . . . 9 |
22 | 21 | comcom5 458 | . . . . . . . 8 |
23 | 19, 22 | fh4r 476 | . . . . . . 7 |
24 | 23 | lor 70 | . . . . . 6 |
25 | orabs 120 | . . . . . . . . . 10 | |
26 | df-a 40 | . . . . . . . . . . . 12 | |
27 | 26 | lor 70 | . . . . . . . . . . 11 |
28 | df-t 41 | . . . . . . . . . . . 12 | |
29 | 28 | ax-r1 35 | . . . . . . . . . . 11 |
30 | 27, 29 | ax-r2 36 | . . . . . . . . . 10 |
31 | 25, 30 | 2an 79 | . . . . . . . . 9 |
32 | an1 106 | . . . . . . . . 9 | |
33 | 31, 32 | ax-r2 36 | . . . . . . . 8 |
34 | 33 | lor 70 | . . . . . . 7 |
35 | ax-a2 31 | . . . . . . 7 | |
36 | 34, 35 | ax-r2 36 | . . . . . 6 |
37 | 24, 36 | ax-r2 36 | . . . . 5 |
38 | 18, 37 | ax-r2 36 | . . . 4 |
39 | 17, 38 | ax-r2 36 | . . 3 |
40 | 6, 39 | ax-r2 36 | . 2 |
41 | 1, 40 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 wi1 12 |
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-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: ud1 595 |
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