HOLE Home Higher-Order Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HOLE Home  >  Th. List  >  wor GIF version

Theorem wor 140
Description: Disjunction type. (Contributed by Mario Carneiro, 8-Oct-2014.)
Assertion
Ref Expression
wor :(∗ → (∗ → ∗))

Proof of Theorem wor
Dummy variables p q x are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wal 134 . . . . 5 :((∗ → ∗) → ∗)
2 wim 137 . . . . . . 7 ⇒ :(∗ → (∗ → ∗))
3 wv 64 . . . . . . . 8 p:∗:∗
4 wv 64 . . . . . . . 8 x:∗:∗
52, 3, 4wov 72 . . . . . . 7 [p:∗ ⇒ x:∗]:∗
6 wv 64 . . . . . . . . 9 q:∗:∗
72, 6, 4wov 72 . . . . . . . 8 [q:∗ ⇒ x:∗]:∗
82, 7, 4wov 72 . . . . . . 7 [[q:∗ ⇒ x:∗] ⇒ x:∗]:∗
92, 5, 8wov 72 . . . . . 6 [[p:∗ ⇒ x:∗] ⇒ [[q:∗ ⇒ x:∗] ⇒ x:∗]]:∗
109wl 66 . . . . 5 λx:∗ [[p:∗ ⇒ x:∗] ⇒ [[q:∗ ⇒ x:∗] ⇒ x:∗]]:(∗ → ∗)
111, 10wc 50 . . . 4 (λx:∗ [[p:∗ ⇒ x:∗] ⇒ [[q:∗ ⇒ x:∗] ⇒ x:∗]]):∗
1211wl 66 . . 3 λq:∗ (λx:∗ [[p:∗ ⇒ x:∗] ⇒ [[q:∗ ⇒ x:∗] ⇒ x:∗]]):(∗ → ∗)
1312wl 66 . 2 λp:∗ λq:∗ (λx:∗ [[p:∗ ⇒ x:∗] ⇒ [[q:∗ ⇒ x:∗] ⇒ x:∗]]):(∗ → (∗ → ∗))
14 df-or 132 . 2 ⊤⊧[ = λp:∗ λq:∗ (λx:∗ [[p:∗ ⇒ x:∗] ⇒ [[q:∗ ⇒ x:∗] ⇒ x:∗]])]
1513, 14eqtypri 81 1 :(∗ → (∗ → ∗))
Colors of variables: type var term
Syntax hints:  tv 1  ht 2  hb 3  kc 5  λkl 6  kt 8  [kbr 9  wffMMJ2t 12  tim 121  tal 122   tor 124
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-an 128  df-im 129  df-or 132
This theorem is referenced by:  orval  147  olc  164  orc  165  exmid  199
  Copyright terms: Public domain W3C validator