Higher-Order Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HOLE Home  >  Th. List  >  wan Structured version   Unicode version

Theorem wan 126
 Description: Conjunction type.
Assertion
Ref Expression
wan

Proof of Theorem wan
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wv 58 . . . . . . 7
2 wv 58 . . . . . . 7
3 wv 58 . . . . . . 7
41, 2, 3wov 64 . . . . . 6
54wl 59 . . . . 5
6 wtru 40 . . . . . . 7
71, 6, 6wov 64 . . . . . 6
87wl 59 . . . . 5
95, 8weqi 68 . . . 4
109wl 59 . . 3
1110wl 59 . 2
12 df-an 118 . 2
1311, 12eqtypri 71 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kl 6   ke 7  kt 8  kbr 9  wffMMJ2t 12   tan 109 This theorem is referenced by:  wim  127  imval  136  anval  138  dfan2  144  hbct  145  ex  148  axrep  207  axun  209 This theorem was proved from axioms:  ax-cb1 29  ax-refl 39 This theorem depends on definitions:  df-an 118
 Copyright terms: Public domain W3C validator