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Theorem anval 148
 Description: Value of the conjunction. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypotheses
Ref Expression
imval.1
imval.2
Assertion
Ref Expression
anval
Distinct variable groups:   ,   ,

Proof of Theorem anval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wan 136 . . 3
2 imval.1 . . 3
3 imval.2 . . 3
41, 2, 3wov 72 . 2
5 df-an 128 . . 3
61, 2, 3, 5oveq 102 . 2
7 wv 64 . . . . . 6
8 wv 64 . . . . . 6
9 wv 64 . . . . . 6
107, 8, 9wov 72 . . . . 5
1110wl 66 . . . 4
12 wtru 43 . . . . . 6
137, 12, 12wov 72 . . . . 5
1413wl 66 . . . 4
1511, 14weqi 76 . . 3
16 weq 41 . . . 4
178, 2weqi 76 . . . . . . 7
1817id 25 . . . . . 6
197, 8, 9, 18oveq1 99 . . . . 5
2010, 19leq 91 . . . 4
2116, 11, 14, 20oveq1 99 . . 3
227, 2, 9wov 72 . . . . 5
2322wl 66 . . . 4
249, 3weqi 76 . . . . . . 7
2524id 25 . . . . . 6
267, 2, 9, 25oveq2 101 . . . . 5
2722, 26leq 91 . . . 4
2816, 23, 14, 27oveq1 99 . . 3
2915, 2, 3, 21, 28ovl 117 . 2
304, 6, 29eqtri 95 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  hb 3  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12   tan 119 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-an 128 This theorem is referenced by:  dfan2  154
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