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Theorem ovl 107

Description: Evaluate a lambda expression in a binary operation.

Hypotheses

Ref	Expression
ovl.1
ovl.2
ovl.3
ovl.4
ovl.5

Assertion

Ref	Expression
ovl

Distinct variable groups:   ,   ,   ,,   ,   ,   ,

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Proof of Theorem ovl

Step	Hyp	Ref	Expression
1		ovl.1	. . . . 5
2	1	wl 59	. . . 4
3	2	wl 59	. . 3
4		ovl.2	. . 3
5		ovl.3	. . 3
6	3, 4, 5	wov 64	. 2
7		weq 38	. . . 4
8	3, 4	wc 45	. . . . 5
9	8, 5	wc 45	. . . 4
10		wtru 40	. . . . 5
11	3, 4, 5	df-ov 65	. . . . 5
12	10, 11	a1i 28	. . . 4
13	7, 6, 9, 12	dfov2 67	. . 3
14	1, 4	distrl 84	. . . . 5
15	10, 14	a1i 28	. . . 4
16	8, 5, 15	ceq1 79	. . 3
17	6, 13, 16	eqtri 85	. 2
18	1	wl 59	. . . 4
19	18, 4	wc 45	. . 3
20		wv 58	. . . . . 6
21	20, 5	weqi 68	. . . . 5
22		ovl.4	. . . . . 6
23	1, 4, 22	cl 106	. . . . 5
24	21, 23	a1i 28	. . . 4
25		ovl.5	. . . 4
26	19, 24, 25	eqtri 85	. . 3
27	19, 5, 26	cl 106	. 2
28	6, 17, 27	eqtri 85	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-refl 39  ax-eqmp 42  ax-ceq 46  ax-beta 60  ax-distrc 61  ax-leq 62  ax-distrl 63  ax-hbl1 93  ax-17 95  ax-inst 103

This theorem depends on definitions:  df-ov 65

This theorem is referenced by:  imval  136  orval  137  anval  138  dfan2  144

Copyright terms: Public domain

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