Higher-Order Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HOLE Home > Th. List > notnot1 | Unicode version |
Description: One side of notnot 187. |
Ref | Expression |
---|---|
notval2.1 |
Ref | Expression |
---|---|
notnot1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wfal 125 | . . . 4 | |
2 | notval2.1 | . . . . 5 | |
3 | wnot 128 | . . . . . 6 | |
4 | 3, 2 | wc 45 | . . . . 5 |
5 | 2, 4 | simpl 22 | . . . 4 |
6 | 2, 4 | simpr 23 | . . . . 5 |
7 | 5 | ax-cb1 29 | . . . . . 6 |
8 | 2 | notval 135 | . . . . . 6 |
9 | 7, 8 | a1i 28 | . . . . 5 |
10 | 6, 9 | mpbi 72 | . . . 4 |
11 | 1, 5, 10 | mpd 146 | . . 3 |
12 | 11 | ex 148 | . 2 |
13 | 4 | notval 135 | . . 3 |
14 | 2, 13 | a1i 28 | . 2 |
15 | 12, 14 | mpbir 77 | 1 |
Colors of variables: type var term |
Syntax hints: hb 3 kc 5 ke 7 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tfal 108 tne 110 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-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-fal 117 df-an 118 df-im 119 df-not 120 |
This theorem is referenced by: con3d 152 exnal1 175 notnot 187 ax9 199 |
Copyright terms: Public domain | W3C validator |