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Mirrors > Home > HOLE Home > Th. List > orval | Unicode version |
Description: Value of the disjunction. |
Ref | Expression |
---|---|
imval.1 | |
imval.2 |
Ref | Expression |
---|---|
orval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wor 130 | . . 3 | |
2 | imval.1 | . . 3 | |
3 | imval.2 | . . 3 | |
4 | 1, 2, 3 | wov 64 | . 2 |
5 | df-or 122 | . . 3 | |
6 | 1, 2, 3, 5 | oveq 92 | . 2 |
7 | wal 124 | . . . 4 | |
8 | wim 127 | . . . . . 6 | |
9 | wv 58 | . . . . . . 7 | |
10 | wv 58 | . . . . . . 7 | |
11 | 8, 9, 10 | wov 64 | . . . . . 6 |
12 | wv 58 | . . . . . . . 8 | |
13 | 8, 12, 10 | wov 64 | . . . . . . 7 |
14 | 8, 13, 10 | wov 64 | . . . . . 6 |
15 | 8, 11, 14 | wov 64 | . . . . 5 |
16 | 15 | wl 59 | . . . 4 |
17 | 7, 16 | wc 45 | . . 3 |
18 | 9, 2 | weqi 68 | . . . . . . . 8 |
19 | 18 | id 25 | . . . . . . 7 |
20 | 8, 9, 10, 19 | oveq1 89 | . . . . . 6 |
21 | 8, 11, 14, 20 | oveq1 89 | . . . . 5 |
22 | 15, 21 | leq 81 | . . . 4 |
23 | 7, 16, 22 | ceq2 80 | . . 3 |
24 | 8, 2, 10 | wov 64 | . . . . . 6 |
25 | 8, 24, 14 | wov 64 | . . . . 5 |
26 | 25 | wl 59 | . . . 4 |
27 | 12, 3 | weqi 68 | . . . . . . . . 9 |
28 | 27 | id 25 | . . . . . . . 8 |
29 | 8, 12, 10, 28 | oveq1 89 | . . . . . . 7 |
30 | 8, 13, 10, 29 | oveq1 89 | . . . . . 6 |
31 | 8, 24, 14, 30 | oveq2 91 | . . . . 5 |
32 | 25, 31 | leq 81 | . . . 4 |
33 | 7, 26, 32 | ceq2 80 | . . 3 |
34 | 17, 2, 3, 23, 33 | ovl 107 | . 2 |
35 | 4, 6, 34 | eqtri 85 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 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-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: ecase 153 olc 154 orc 155 |
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