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Mirrors > Home > QLE Home > Th. List > bi1o1a | Unicode version |
Description: Equivalence to biconditional. |
Ref | Expression |
---|---|
bi1o1a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lea 160 | . . . . . . 7 | |
2 | leo 158 | . . . . . . 7 | |
3 | 1, 2 | letr 137 | . . . . . 6 |
4 | 3 | lecom 180 | . . . . 5 |
5 | 4 | comcom 453 | . . . 4 |
6 | comor1 461 | . . . . 5 | |
7 | 6 | comcom7 460 | . . . 4 |
8 | 5, 7 | fh1 469 | . . 3 |
9 | 8 | ax-r1 35 | . 2 |
10 | dfb 94 | . . 3 | |
11 | ax-a2 31 | . . 3 | |
12 | leid 148 | . . . . . 6 | |
13 | 3, 12 | ler2an 173 | . . . . 5 |
14 | lear 161 | . . . . 5 | |
15 | 13, 14 | lebi 145 | . . . 4 |
16 | dff 101 | . . . . . . 7 | |
17 | ancom 74 | . . . . . . 7 | |
18 | 16, 17 | ax-r2 36 | . . . . . 6 |
19 | 18 | ax-r5 38 | . . . . 5 |
20 | lea 160 | . . . . . . . 8 | |
21 | 20 | df2le2 136 | . . . . . . 7 |
22 | 21 | ax-r1 35 | . . . . . 6 |
23 | or0r 103 | . . . . . . 7 | |
24 | 23 | ax-r1 35 | . . . . . 6 |
25 | 22, 24 | ax-r2 36 | . . . . 5 |
26 | comid 187 | . . . . . . 7 | |
27 | 26 | comcom2 183 | . . . . . 6 |
28 | comanr1 464 | . . . . . 6 | |
29 | 27, 28 | fh1r 473 | . . . . 5 |
30 | 19, 25, 29 | 3tr1 63 | . . . 4 |
31 | 15, 30 | 2or 72 | . . 3 |
32 | 10, 11, 31 | 3tr 65 | . 2 |
33 | df-i1 44 | . . . 4 | |
34 | lear 161 | . . . . . 6 | |
35 | leid 148 | . . . . . . 7 | |
36 | 20, 35 | ler2an 173 | . . . . . 6 |
37 | 34, 36 | lebi 145 | . . . . 5 |
38 | 37 | lor 70 | . . . 4 |
39 | 33, 38 | ax-r2 36 | . . 3 |
40 | df-i1 44 | . . . 4 | |
41 | anor3 90 | . . . . . 6 | |
42 | 41 | ax-r1 35 | . . . . 5 |
43 | lear 161 | . . . . . 6 | |
44 | leo 158 | . . . . . . 7 | |
45 | leid 148 | . . . . . . 7 | |
46 | 44, 45 | ler2an 173 | . . . . . 6 |
47 | 43, 46 | lebi 145 | . . . . 5 |
48 | 42, 47 | 2or 72 | . . . 4 |
49 | 40, 48 | ax-r2 36 | . . 3 |
50 | 39, 49 | 2an 79 | . 2 |
51 | 9, 32, 50 | 3tr1 63 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 tb 5 wo 6 wa 7 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 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: mlaconj 845 |
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