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.

Step	Hyp	Ref	Expression
1		wim 137	. . . 4 ⊢ ⇒ :(∗ → (∗ → ∗))
2		wv 64	. . . 4 ⊢ p:∗:∗
3		wfal 135	. . . 4 ⊢ ⊥:∗
4	1, 2, 3	wov 72	. . 3 ⊢ [p:∗ ⇒ ⊥]:∗
5	4	wl 66	. 2 ⊢ λp:∗ [p:∗ ⇒ ⊥]:(∗ → ∗)
6		df-not 130	. 2 ⊢ ⊤⊧[¬ = λp:∗ [p:∗ ⇒ ⊥]]
7	5, 6	eqtypri 81	1 ⊢ ¬ :(∗ → ∗)

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