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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 |- A.:((* -> *) -> *)
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 |- \x:* [[p:* ==> x:*] ==> [[q:* ==> x:*] ==> x:*]]:(* -> *)
111, 10wc 50 . . . 4 |- (A.\x:* [[p:* ==> x:*] ==> [[q:* ==> x:*] ==> x:*]]):*
1211wl 66 . . 3 |- \q:* (A.\x:* [[p:* ==> x:*] ==> [[q:* ==> x:*] ==> x:*]]):(* -> *)
1312wl 66 . 2 |- \p:* \q:* (A.\x:* [[p:* ==> x:*] ==> [[q:* ==> x:*] ==> x:*]]):(* -> (* -> *))
14 df-or 132 . 2 |- T. |= [ \/ = \p:* \q:* (A.\x:* [[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  \kl 6  T.kt 8  [kbr 9  wffMMJ2t 12   ==> tim 121  A.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
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