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Mirrors > Home > HOLE Home > Th. List > imval | Unicode version |
Description: Value of the implication. |
Ref | Expression |
---|---|
imval.1 | |
imval.2 |
Ref | Expression |
---|---|
imval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wim 127 | . . 3 | |
2 | imval.1 | . . 3 | |
3 | imval.2 | . . 3 | |
4 | 1, 2, 3 | wov 64 | . 2 |
5 | df-im 119 | . . 3 | |
6 | 1, 2, 3, 5 | oveq 92 | . 2 |
7 | wan 126 | . . . . 5 | |
8 | wv 58 | . . . . 5 | |
9 | wv 58 | . . . . 5 | |
10 | 7, 8, 9 | wov 64 | . . . 4 |
11 | 10, 8 | weqi 68 | . . 3 |
12 | weq 38 | . . . 4 | |
13 | 8, 2 | weqi 68 | . . . . . 6 |
14 | 13 | id 25 | . . . . 5 |
15 | 7, 8, 9, 14 | oveq1 89 | . . . 4 |
16 | 12, 10, 8, 15, 14 | oveq12 90 | . . 3 |
17 | 7, 2, 9 | wov 64 | . . . 4 |
18 | 9, 3 | weqi 68 | . . . . . 6 |
19 | 18 | id 25 | . . . . 5 |
20 | 7, 2, 9, 19 | oveq2 91 | . . . 4 |
21 | 12, 17, 2, 20 | oveq1 89 | . . 3 |
22 | 11, 2, 3, 16, 21 | ovl 107 | . 2 |
23 | 4, 6, 22 | eqtri 85 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 hb 3 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 wffMMJ2t 12 tan 109 tim 111 |
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-an 118 df-im 119 |
This theorem is referenced by: mpd 146 ex 148 |
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