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Mirrors > Home > HOLE Home > Th. List > olc | Unicode version |
Description: Or introduction. |
Ref | Expression |
---|---|
olc.1 | |
olc.2 |
Ref | Expression |
---|---|
olc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wim 127 | . . . 4 | |
2 | olc.1 | . . . . 5 | |
3 | wv 58 | . . . . 5 | |
4 | 1, 2, 3 | wov 64 | . . . 4 |
5 | olc.2 | . . . . . 6 | |
6 | 1, 5, 3 | wov 64 | . . . . 5 |
7 | 1, 6, 3 | wov 64 | . . . 4 |
8 | 1, 4, 7 | wov 64 | . . 3 |
9 | wtru 40 | . . . 4 | |
10 | 5, 6 | simpl 22 | . . . . . . . . 9 |
11 | 5, 6 | simpr 23 | . . . . . . . . 9 |
12 | 3, 10, 11 | mpd 146 | . . . . . . . 8 |
13 | 12 | ex 148 | . . . . . . 7 |
14 | 13, 4 | adantr 50 | . . . . . 6 |
15 | 14 | ex 148 | . . . . 5 |
16 | 15 | eqtru 76 | . . . 4 |
17 | 9, 16 | eqcomi 70 | . . 3 |
18 | 8, 17 | leq 81 | . 2 |
19 | wor 130 | . . . . 5 | |
20 | 19, 2, 5 | wov 64 | . . . 4 |
21 | 2, 5 | orval 137 | . . . 4 |
22 | 8 | wl 59 | . . . . 5 |
23 | 22 | alval 132 | . . . 4 |
24 | 20, 21, 23 | eqtri 85 | . . 3 |
25 | 5, 24 | a1i 28 | . 2 |
26 | 18, 25 | mpbir 77 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tim 111 tal 112 tor 114 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-al 116 df-an 118 df-im 119 df-or 122 |
This theorem is referenced by: exmid 186 |
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