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Mirrors > Home > HOLE Home > Th. List > ecase | Unicode version |
Description: Elimination by cases. |
Ref | Expression |
---|---|
ecase.1 | |
ecase.2 | |
ecase.3 | |
ecase.4 | |
ecase.5 | |
ecase.6 |
Ref | Expression |
---|---|
ecase |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecase.3 | . 2 | |
2 | ecase.6 | . . 3 | |
3 | 2 | ex 148 | . 2 |
4 | wim 127 | . . . 4 | |
5 | ecase.2 | . . . . 5 | |
6 | 4, 5, 1 | wov 64 | . . . 4 |
7 | 4, 6, 1 | wov 64 | . . 3 |
8 | ecase.5 | . . . 4 | |
9 | 8 | ex 148 | . . 3 |
10 | ecase.4 | . . . . 5 | |
11 | 10 | ax-cb1 29 | . . . . . 6 |
12 | ecase.1 | . . . . . . 7 | |
13 | 12, 5 | orval 137 | . . . . . 6 |
14 | 11, 13 | a1i 28 | . . . . 5 |
15 | 10, 14 | mpbi 72 | . . . 4 |
16 | wv 58 | . . . . . . 7 | |
17 | 4, 12, 16 | wov 64 | . . . . . 6 |
18 | 4, 5, 16 | wov 64 | . . . . . . 7 |
19 | 4, 18, 16 | wov 64 | . . . . . 6 |
20 | 4, 17, 19 | wov 64 | . . . . 5 |
21 | 16, 1 | weqi 68 | . . . . . . . 8 |
22 | 21 | id 25 | . . . . . . 7 |
23 | 4, 12, 16, 22 | oveq2 91 | . . . . . 6 |
24 | 4, 5, 16, 22 | oveq2 91 | . . . . . . 7 |
25 | 4, 18, 16, 24, 22 | oveq12 90 | . . . . . 6 |
26 | 4, 17, 19, 23, 25 | oveq12 90 | . . . . 5 |
27 | 20, 1, 26 | cla4v 142 | . . . 4 |
28 | 15, 27 | syl 16 | . . 3 |
29 | 7, 9, 28 | mpd 146 | . 2 |
30 | 1, 3, 29 | mpd 146 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 hb 3 kc 5 kl 6 ke 7 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 notnot 187 ax3 192 |
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