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Theorem wex 129
 Description: There exists type.
Assertion
Ref Expression
wex

Proof of Theorem wex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wal 124 . . . 4
2 wim 127 . . . . . 6
3 wal 124 . . . . . . 7
4 wv 58 . . . . . . . . . 10
5 wv 58 . . . . . . . . . 10
64, 5wc 45 . . . . . . . . 9
7 wv 58 . . . . . . . . 9
82, 6, 7wov 64 . . . . . . . 8
98wl 59 . . . . . . 7
103, 9wc 45 . . . . . 6
112, 10, 7wov 64 . . . . 5
1211wl 59 . . . 4
131, 12wc 45 . . 3
1413wl 59 . 2
15 df-ex 121 . 2
1614, 15eqtypri 71 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 111  tal 112  tex 113 This theorem is referenced by:  weu  131  exval  133  euval  134  exlimdv2  156  exlimd  171  eximdv  173  alnex  174  exnal1  175  exnal  188  ax9  199  axrep  207  axun  209 This theorem was proved from axioms:  ax-cb1 29  ax-refl 39 This theorem depends on definitions:  df-al 116  df-an 118  df-im 119  df-ex 121
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