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Theorem euval 144
 Description: Value of the 'exists unique' predicate. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
alval.1
Assertion
Ref Expression
euval
Distinct variable groups:   ,,   ,,

Proof of Theorem euval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 weu 141 . . 3
2 alval.1 . . 3
31, 2wc 50 . 2
4 df-eu 133 . . 3
51, 2, 4ceq1 89 . 2
6 wex 139 . . . 4
7 wal 134 . . . . . 6
8 wv 64 . . . . . . . . 9
9 wv 64 . . . . . . . . 9
108, 9wc 50 . . . . . . . 8
11 wv 64 . . . . . . . . 9
129, 11weqi 76 . . . . . . . 8
1310, 12weqi 76 . . . . . . 7
1413wl 66 . . . . . 6
157, 14wc 50 . . . . 5
1615wl 66 . . . 4
176, 16wc 50 . . 3
18 weq 41 . . . . . . . 8
198, 2weqi 76 . . . . . . . . . 10
2019id 25 . . . . . . . . 9
218, 9, 20ceq1 89 . . . . . . . 8
2218, 10, 12, 21oveq1 99 . . . . . . 7
2313, 22leq 91 . . . . . 6
247, 14, 23ceq2 90 . . . . 5
2515, 24leq 91 . . . 4
266, 16, 25ceq2 90 . . 3
2717, 2, 26cl 116 . 2
283, 5, 27eqtri 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  tal 122  tex 123  teu 125 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  df-eu 133 This theorem is referenced by: (None)
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