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Theorem orval 147
 Description: Value of the disjunction. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypotheses
Ref Expression
imval.1
imval.2
Assertion
Ref Expression
orval
Distinct variable groups:   ,   ,

Proof of Theorem orval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wor 140 . . 3
2 imval.1 . . 3
3 imval.2 . . 3
41, 2, 3wov 72 . 2
5 df-or 132 . . 3
61, 2, 3, 5oveq 102 . 2
7 wal 134 . . . 4
8 wim 137 . . . . . 6
9 wv 64 . . . . . . 7
10 wv 64 . . . . . . 7
118, 9, 10wov 72 . . . . . 6
12 wv 64 . . . . . . . 8
138, 12, 10wov 72 . . . . . . 7
148, 13, 10wov 72 . . . . . 6
158, 11, 14wov 72 . . . . 5
1615wl 66 . . . 4
177, 16wc 50 . . 3
189, 2weqi 76 . . . . . . . 8
1918id 25 . . . . . . 7
208, 9, 10, 19oveq1 99 . . . . . 6
218, 11, 14, 20oveq1 99 . . . . 5
2215, 21leq 91 . . . 4
237, 16, 22ceq2 90 . . 3
248, 2, 10wov 72 . . . . . 6
258, 24, 14wov 72 . . . . 5
2625wl 66 . . . 4
2712, 3weqi 76 . . . . . . . . 9
2827id 25 . . . . . . . 8
298, 12, 10, 28oveq1 99 . . . . . . 7
308, 13, 10, 29oveq1 99 . . . . . 6
318, 24, 14, 30oveq2 101 . . . . 5
3225, 31leq 91 . . . 4
337, 26, 32ceq2 90 . . 3
3417, 2, 3, 23, 33ovl 117 . 2
354, 6, 34eqtri 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   tor 124 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-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-or 132 This theorem is referenced by:  ecase  163  olc  164  orc  165
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