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Mirrors > Home > HOLE Home > Th. List > wnot | GIF version |
Description: Negation type. |
Ref | Expression |
---|---|
wnot | ⊢ ¬ :(∗ → ∗) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wim 127 | . . . 4 ⊢ ⇒ :(∗ → (∗ → ∗)) | |
2 | wv 58 | . . . 4 ⊢ p:∗:∗ | |
3 | wfal 125 | . . . 4 ⊢ ⊥:∗ | |
4 | 1, 2, 3 | wov 64 | . . 3 ⊢ [p:∗ ⇒ ⊥]:∗ |
5 | 4 | wl 59 | . 2 ⊢ λp:∗ [p:∗ ⇒ ⊥]:(∗ → ∗) |
6 | df-not 120 | . 2 ⊢ ⊤⊧[¬ = λp:∗ [p:∗ ⇒ ⊥]] | |
7 | 5, 6 | eqtypri 71 | 1 ⊢ ¬ :(∗ → ∗) |
Colors of variables: type var term |
Syntax hints: tv 1 → ht 2 ∗hb 3 λkl 6 ⊤kt 8 [kbr 9 wffMMJ2t 12 ⊥tfal 108 ¬ tne 110 ⇒ tim 111 |
This theorem was proved from axioms: ax-cb1 29 ax-refl 39 |
This theorem depends on definitions: df-al 116 df-fal 117 df-an 118 df-im 119 df-not 120 |
This theorem is referenced by: notval 135 notval2 149 notnot1 150 con3d 152 alnex 174 exnal1 175 exmid 186 notnot 187 exnal 188 ax3 192 ax6 195 ax9 199 ax12 202 |
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