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Mirrors > Home > HOLE Home > Th. List > exnal1 | Unicode version |
Description: Forward direction of exnal 188. |
Ref | Expression |
---|---|
alnex1.1 |
Ref | Expression |
---|---|
exnal1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wex 129 | . . . 4 | |
2 | wnot 128 | . . . . . 6 | |
3 | alnex1.1 | . . . . . 6 | |
4 | 2, 3 | wc 45 | . . . . 5 |
5 | 4 | wl 59 | . . . 4 |
6 | 1, 5 | wc 45 | . . 3 |
7 | 3 | notnot1 150 | . . . . . 6 |
8 | wtru 40 | . . . . . 6 | |
9 | 7, 8 | adantl 51 | . . . . 5 |
10 | 9 | alimdv 172 | . . . 4 |
11 | wal 124 | . . . . . . 7 | |
12 | 2, 4 | wc 45 | . . . . . . . 8 |
13 | 12 | wl 59 | . . . . . . 7 |
14 | 11, 13 | wc 45 | . . . . . 6 |
15 | 14 | id 25 | . . . . 5 |
16 | 4 | alnex 174 | . . . . . 6 |
17 | 14, 16 | a1i 28 | . . . . 5 |
18 | 15, 17 | mpbi 72 | . . . 4 |
19 | 10, 18 | syl 16 | . . 3 |
20 | 6, 19 | con2d 151 | . 2 |
21 | 20 | trul 37 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tne 110 tal 112 tex 113 |
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 ax-eta 165 |
This theorem depends on definitions: df-ov 65 df-al 116 df-fal 117 df-an 118 df-im 119 df-not 120 df-ex 121 |
This theorem is referenced by: (None) |
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