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Mirrors > Home > QLE Home > Th. List > u2lemle2 | Unicode version |
Description: Dishkant implication to l.e. |
Ref | Expression |
---|---|
u2lemle2.1 |
Ref | Expression |
---|---|
u2lemle2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-a2 31 | . . . . . . 7 | |
2 | 1 | lan 77 | . . . . . 6 |
3 | coman1 185 | . . . . . . . . 9 | |
4 | 3 | comcom7 460 | . . . . . . . 8 |
5 | coman2 186 | . . . . . . . . 9 | |
6 | 5 | comcom7 460 | . . . . . . . 8 |
7 | 4, 6 | fh2 470 | . . . . . . 7 |
8 | ancom 74 | . . . . . . . . . 10 | |
9 | anass 76 | . . . . . . . . . 10 | |
10 | dff 101 | . . . . . . . . . . . . 13 | |
11 | 10 | ax-r1 35 | . . . . . . . . . . . 12 |
12 | 11 | lan 77 | . . . . . . . . . . 11 |
13 | an0 108 | . . . . . . . . . . 11 | |
14 | 12, 13 | ax-r2 36 | . . . . . . . . . 10 |
15 | 8, 9, 14 | 3tr2 64 | . . . . . . . . 9 |
16 | 15 | ax-r5 38 | . . . . . . . 8 |
17 | ax-a2 31 | . . . . . . . 8 | |
18 | 16, 17 | ax-r2 36 | . . . . . . 7 |
19 | 7, 18 | ax-r2 36 | . . . . . 6 |
20 | 2, 19 | ax-r2 36 | . . . . 5 |
21 | 20 | ax-r1 35 | . . . 4 |
22 | df-i2 45 | . . . . . . 7 | |
23 | 22 | ax-r1 35 | . . . . . 6 |
24 | u2lemle2.1 | . . . . . 6 | |
25 | 23, 24 | ax-r2 36 | . . . . 5 |
26 | 25 | lan 77 | . . . 4 |
27 | 21, 26 | ax-r2 36 | . . 3 |
28 | or0 102 | . . 3 | |
29 | an1 106 | . . 3 | |
30 | 27, 28, 29 | 3tr2 64 | . 2 |
31 | 30 | df2le1 135 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wn 4 wo 6 wa 7 wt 8 wf 9 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-i2 45 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: 3vroa 831 imp3 841 |
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