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Theorem wex 139
 Description: There exists type. (Contributed by Mario Carneiro, 8-Oct-2014.)
Assertion
Ref Expression
wex

Proof of Theorem wex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wal 134 . . . 4
2 wim 137 . . . . . 6
3 wal 134 . . . . . . 7
4 wv 64 . . . . . . . . . 10
5 wv 64 . . . . . . . . . 10
64, 5wc 50 . . . . . . . . 9
7 wv 64 . . . . . . . . 9
82, 6, 7wov 72 . . . . . . . 8
98wl 66 . . . . . . 7
103, 9wc 50 . . . . . 6
112, 10, 7wov 72 . . . . 5
1211wl 66 . . . 4
131, 12wc 50 . . 3
1413wl 66 . 2
15 df-ex 131 . 2
1614, 15eqtypri 81 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kc 5  kl 6  kt 8  kbr 9  wffMMJ2t 12   tim 121  tal 122  tex 123 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-ex 131 This theorem is referenced by:  weu  141  exval  143  euval  144  exlimdv2  166  exlimd  183  eximdv  185  alnex  186  exnal1  187  exnal  201  ax9  212  axrep  220  axun  222
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