Quantum Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > QLE Home > Th. List > oa3-2lema | Unicode version |
Description: Lemma for 3-OA(2). Equivalence with substitution into 4-OA. |
Ref | Expression |
---|---|
oa3-2lema |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-a3 32 | . . . . 5 | |
2 | an0 108 | . . . . . . . . . . 11 | |
3 | 2 | ax-r5 38 | . . . . . . . . . 10 |
4 | ax-a2 31 | . . . . . . . . . 10 | |
5 | or0 102 | . . . . . . . . . . 11 | |
6 | 0i1 273 | . . . . . . . . . . . 12 | |
7 | 6 | lan 77 | . . . . . . . . . . 11 |
8 | an1 106 | . . . . . . . . . . 11 | |
9 | 5, 7, 8 | 3tr 65 | . . . . . . . . . 10 |
10 | 3, 4, 9 | 3tr 65 | . . . . . . . . 9 |
11 | an0 108 | . . . . . . . . . . 11 | |
12 | 11 | ax-r5 38 | . . . . . . . . . 10 |
13 | ax-a2 31 | . . . . . . . . . 10 | |
14 | or0 102 | . . . . . . . . . . 11 | |
15 | 6 | lan 77 | . . . . . . . . . . 11 |
16 | an1 106 | . . . . . . . . . . 11 | |
17 | 14, 15, 16 | 3tr 65 | . . . . . . . . . 10 |
18 | 12, 13, 17 | 3tr 65 | . . . . . . . . 9 |
19 | 10, 18 | 2an 79 | . . . . . . . 8 |
20 | 19 | lor 70 | . . . . . . 7 |
21 | oridm 110 | . . . . . . 7 | |
22 | 20, 21 | ax-r2 36 | . . . . . 6 |
23 | 22 | lor 70 | . . . . 5 |
24 | 1, 23 | ax-r2 36 | . . . 4 |
25 | 24 | lan 77 | . . 3 |
26 | 25 | lor 70 | . 2 |
27 | 26 | lan 77 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wo 6 wa 7 wt 8 wf 9 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 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-i1 44 |
This theorem is referenced by: oa3-2to2s 990 |
Copyright terms: Public domain | W3C validator |