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Theorem imval 146
 Description: Value of the implication. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypotheses
Ref Expression
imval.1
imval.2
Assertion
Ref Expression
imval

Proof of Theorem imval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wim 137 . . 3
2 imval.1 . . 3
3 imval.2 . . 3
41, 2, 3wov 72 . 2
5 df-im 129 . . 3
61, 2, 3, 5oveq 102 . 2
7 wan 136 . . . . 5
8 wv 64 . . . . 5
9 wv 64 . . . . 5
107, 8, 9wov 72 . . . 4
1110, 8weqi 76 . . 3
12 weq 41 . . . 4
138, 2weqi 76 . . . . . 6
1413id 25 . . . . 5
157, 8, 9, 14oveq1 99 . . . 4
1612, 10, 8, 15, 14oveq12 100 . . 3
177, 2, 9wov 72 . . . 4
189, 3weqi 76 . . . . . 6
1918id 25 . . . . 5
207, 2, 9, 19oveq2 101 . . . 4
2112, 17, 2, 20oveq1 99 . . 3
2211, 2, 3, 16, 21ovl 117 . 2
234, 6, 22eqtri 95 1
 Colors of variables: type var term Syntax hints:  tv 1  hb 3  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12   tan 119   tim 121 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  df-im 129 This theorem is referenced by:  mpd  156  ex  158
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