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Mirrors > Home > HOLE Home > Th. List > ovl | Unicode version |
Description: Evaluate a lambda expression in a binary operation. |
Ref | Expression |
---|---|
ovl.1 | |
ovl.2 | |
ovl.3 | |
ovl.4 | |
ovl.5 |
Ref | Expression |
---|---|
ovl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovl.1 | . . . . 5 | |
2 | 1 | wl 59 | . . . 4 |
3 | 2 | wl 59 | . . 3 |
4 | ovl.2 | . . 3 | |
5 | ovl.3 | . . 3 | |
6 | 3, 4, 5 | wov 64 | . 2 |
7 | weq 38 | . . . 4 | |
8 | 3, 4 | wc 45 | . . . . 5 |
9 | 8, 5 | wc 45 | . . . 4 |
10 | wtru 40 | . . . . 5 | |
11 | 3, 4, 5 | df-ov 65 | . . . . 5 |
12 | 10, 11 | a1i 28 | . . . 4 |
13 | 7, 6, 9, 12 | dfov2 67 | . . 3 |
14 | 1, 4 | distrl 84 | . . . . 5 |
15 | 10, 14 | a1i 28 | . . . 4 |
16 | 8, 5, 15 | ceq1 79 | . . 3 |
17 | 6, 13, 16 | eqtri 85 | . 2 |
18 | 1 | wl 59 | . . . 4 |
19 | 18, 4 | wc 45 | . . 3 |
20 | wv 58 | . . . . . 6 | |
21 | 20, 5 | weqi 68 | . . . . 5 |
22 | ovl.4 | . . . . . 6 | |
23 | 1, 4, 22 | cl 106 | . . . . 5 |
24 | 21, 23 | a1i 28 | . . . 4 |
25 | ovl.5 | . . . 4 | |
26 | 19, 24, 25 | eqtri 85 | . . 3 |
27 | 19, 5, 26 | cl 106 | . 2 |
28 | 6, 17, 27 | eqtri 85 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 kc 5 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 wffMMJ2t 12 |
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 |
This theorem is referenced by: imval 136 orval 137 anval 138 dfan2 144 |
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