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Theorem exlimdv 167
 Description: Existential elimination. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypothesis
Ref Expression
exlimdv.1
Assertion
Ref Expression
exlimdv
Distinct variable groups:   ,   ,   ,

Proof of Theorem exlimdv
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 exlimdv.1 . . . . 5
21ax-cb1 29 . . . 4
32wctr 34 . . 3
43wl 66 . 2
5 wv 64 . . . 4
64, 5wc 50 . . 3
71ax-cb2 30 . . 3
8 wim 137 . . . . 5
98, 6, 7wov 72 . . . 4
101ex 158 . . . 4
11 wv 64 . . . . 5
128, 11ax-17 105 . . . . 5
133, 11ax-hbl1 103 . . . . . 6
145, 11ax-17 105 . . . . . 6
154, 5, 11, 13, 14hbc 110 . . . . 5
167, 11ax-17 105 . . . . 5
178, 6, 11, 7, 12, 15, 16hbov 111 . . . 4
18 wv 64 . . . . . . . 8
1918, 5weqi 76 . . . . . . 7
204, 18wc 50 . . . . . . . 8
213beta 92 . . . . . . . 8
2220, 21eqcomi 79 . . . . . . 7
2319, 22a1i 28 . . . . . 6
2419id 25 . . . . . . 7
254, 18, 24ceq2 90 . . . . . 6
263, 23, 25eqtri 95 . . . . 5
278, 3, 7, 26oveq1 99 . . . 4
285, 9, 10, 17, 27insti 114 . . 3
296, 7, 28imp 157 . 2
304, 29exlimdv2 166 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  kct 10   wffMMJ2 11   tim 121  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-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-distrl 70  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: (None)
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