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Theorem exval 143
 Description: Value of the 'there exists' predicate. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
alval.1
Assertion
Ref Expression
exval
Distinct variable groups:   ,,   ,,

Proof of Theorem exval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 wex 139 . . 3
2 alval.1 . . 3
31, 2wc 50 . 2
4 df-ex 131 . . 3
51, 2, 4ceq1 89 . 2
6 wal 134 . . . 4
7 wim 137 . . . . . 6
8 wal 134 . . . . . . 7
9 wv 64 . . . . . . . . . 10
10 wv 64 . . . . . . . . . 10
119, 10wc 50 . . . . . . . . 9
12 wv 64 . . . . . . . . 9
137, 11, 12wov 72 . . . . . . . 8
1413wl 66 . . . . . . 7
158, 14wc 50 . . . . . 6
167, 15, 12wov 72 . . . . 5
1716wl 66 . . . 4
186, 17wc 50 . . 3
199, 2weqi 76 . . . . . . . . . . 11
2019id 25 . . . . . . . . . 10
219, 10, 20ceq1 89 . . . . . . . . 9
227, 11, 12, 21oveq1 99 . . . . . . . 8
2313, 22leq 91 . . . . . . 7
248, 14, 23ceq2 90 . . . . . 6
257, 15, 12, 24oveq1 99 . . . . 5
2616, 25leq 91 . . . 4
276, 17, 26ceq2 90 . . 3
2818, 2, 27cl 116 . 2
293, 5, 28eqtri 95 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kc 5  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12   tim 121  tal 122  tex 123 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113 This theorem depends on definitions:  df-ov 73  df-al 126  df-an 128  df-im 129  df-ex 131 This theorem is referenced by:  exlimdv2  166  ax4e  168  exlimd  183
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