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Theorem ovl 117
 Description: Evaluate a lambda expression in a binary operation. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
ovl.1
ovl.2
ovl.3
ovl.4
ovl.5
Assertion
Ref Expression
ovl
Distinct variable groups:   ,   ,   ,,   ,   ,   ,

Proof of Theorem ovl
StepHypRef Expression
1 ovl.1 . . . . 5
21wl 66 . . . 4
32wl 66 . . 3
4 ovl.2 . . 3
5 ovl.3 . . 3
63, 4, 5wov 72 . 2
7 weq 41 . . . 4
83, 4wc 50 . . . . 5
98, 5wc 50 . . . 4
10 wtru 43 . . . . 5
113, 4, 5df-ov 73 . . . . 5
1210, 11a1i 28 . . . 4
137, 6, 9, 12dfov2 75 . . 3
141, 4distrl 94 . . . . 5
1510, 14a1i 28 . . . 4
168, 5, 15ceq1 89 . . 3
176, 13, 16eqtri 95 . 2
181wl 66 . . . 4
1918, 4wc 50 . . 3
20 wv 64 . . . . . 6
2120, 5weqi 76 . . . . 5
22 ovl.4 . . . . . 6
231, 4, 22cl 116 . . . . 5
2421, 23a1i 28 . . . 4
25 ovl.5 . . . 4
2619, 24, 25eqtri 95 . . 3
2719, 5, 26cl 116 . 2
286, 17, 27eqtri 95 1
 Colors of variables: type var term Syntax hints:  tv 1   ht 2  kc 5  kl 6   ke 7  kt 8  kbr 9   wffMMJ2 11  wffMMJ2t 12 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 This theorem is referenced by:  imval  146  orval  147  anval  148  dfan2  154
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