Quantum Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > QLE Home > Th. List > u3lemaa | Unicode version |
Description: Lemma for Kalmbach implication study. |
Ref | Expression |
---|---|
u3lemaa |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i3 46 | . . 3 | |
2 | 1 | ran 78 | . 2 |
3 | comanr1 464 | . . . . . 6 | |
4 | 3 | comcom6 459 | . . . . 5 |
5 | comanr1 464 | . . . . . 6 | |
6 | 5 | comcom6 459 | . . . . 5 |
7 | 4, 6 | com2or 483 | . . . 4 |
8 | comid 187 | . . . . 5 | |
9 | comorr 184 | . . . . . 6 | |
10 | 9 | comcom6 459 | . . . . 5 |
11 | 8, 10 | com2an 484 | . . . 4 |
12 | 7, 11 | fh1r 473 | . . 3 |
13 | 4, 6 | fh1r 473 | . . . . . 6 |
14 | ancom 74 | . . . . . . . . 9 | |
15 | anass 76 | . . . . . . . . . . 11 | |
16 | 15 | ax-r1 35 | . . . . . . . . . 10 |
17 | ancom 74 | . . . . . . . . . . 11 | |
18 | dff 101 | . . . . . . . . . . . . . 14 | |
19 | 18 | ax-r1 35 | . . . . . . . . . . . . 13 |
20 | 19 | lan 77 | . . . . . . . . . . . 12 |
21 | an0 108 | . . . . . . . . . . . 12 | |
22 | 20, 21 | ax-r2 36 | . . . . . . . . . . 11 |
23 | 17, 22 | ax-r2 36 | . . . . . . . . . 10 |
24 | 16, 23 | ax-r2 36 | . . . . . . . . 9 |
25 | 14, 24 | ax-r2 36 | . . . . . . . 8 |
26 | ancom 74 | . . . . . . . . 9 | |
27 | anass 76 | . . . . . . . . . . 11 | |
28 | 27 | ax-r1 35 | . . . . . . . . . 10 |
29 | ancom 74 | . . . . . . . . . . 11 | |
30 | 19 | lan 77 | . . . . . . . . . . . 12 |
31 | an0 108 | . . . . . . . . . . . 12 | |
32 | 30, 31 | ax-r2 36 | . . . . . . . . . . 11 |
33 | 29, 32 | ax-r2 36 | . . . . . . . . . 10 |
34 | 28, 33 | ax-r2 36 | . . . . . . . . 9 |
35 | 26, 34 | ax-r2 36 | . . . . . . . 8 |
36 | 25, 35 | 2or 72 | . . . . . . 7 |
37 | or0 102 | . . . . . . 7 | |
38 | 36, 37 | ax-r2 36 | . . . . . 6 |
39 | 13, 38 | ax-r2 36 | . . . . 5 |
40 | an32 83 | . . . . . 6 | |
41 | anidm 111 | . . . . . . 7 | |
42 | 41 | ran 78 | . . . . . 6 |
43 | 40, 42 | ax-r2 36 | . . . . 5 |
44 | 39, 43 | 2or 72 | . . . 4 |
45 | ax-a2 31 | . . . . 5 | |
46 | or0 102 | . . . . 5 | |
47 | 45, 46 | ax-r2 36 | . . . 4 |
48 | 44, 47 | ax-r2 36 | . . 3 |
49 | 12, 48 | ax-r2 36 | . 2 |
50 | 2, 49 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wf 9 wi3 14 |
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-i3 46 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: u3lemnona 667 u3lem13b 790 |
Copyright terms: Public domain | W3C validator |