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Theorem wnot 138
 Description: Negation type. (Contributed by Mario Carneiro, 8-Oct-2014.)
Assertion
Ref Expression
wnot ¬ :(∗ → ∗)

Proof of Theorem wnot
Dummy variable p is distinct from all other variables.
StepHypRef Expression
1 wim 137 . . . 4 ⇒ :(∗ → (∗ → ∗))
2 wv 64 . . . 4 p:∗:∗
3 wfal 135 . . . 4 ⊥:∗
41, 2, 3wov 72 . . 3 [p:∗ ⇒ ⊥]:∗
54wl 66 . 2 λp:∗ [p:∗ ⇒ ⊥]:(∗ → ∗)
6 df-not 130 . 2 ⊤⊧[¬ = λp:∗ [p:∗ ⇒ ⊥]]
75, 6eqtypri 81 1 ¬ :(∗ → ∗)
 Colors of variables: type var term Syntax hints:  tv 1   → ht 2  ∗hb 3  λkl 6  ⊤kt 8  [kbr 9  wffMMJ2t 12  ⊥tfal 118  ¬ tne 120   ⇒ tim 121 This theorem was proved from axioms:  ax-cb1 29  ax-weq 40  ax-refl 42  ax-wc 49  ax-wv 63  ax-wl 65  ax-wov 71  ax-eqtypri 80 This theorem depends on definitions:  df-al 126  df-fal 127  df-an 128  df-im 129  df-not 130 This theorem is referenced by:  notval  145  notval2  159  notnot1  160  con3d  162  alnex  186  exnal1  187  exmid  199  notnot  200  exnal  201  ax3  205  ax6  208  ax9  212  ax12  215
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