imval - Higher-Order Logic Explorer

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Theorem imval 136

Description: Value of the implication.

**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.

Step	Hyp	Ref	Expression
1		wim 127	. . 3
2		imval.1	. . 3
3		imval.2	. . 3
4	1, 2, 3	wov 64	. 2
5		df-im 119	. . 3 $/\$
6	1, 2, 3, 5	oveq 92	. 2 $/\$
7		wan 126	. . . . 5 $/\$
8		wv 58	. . . . 5
9		wv 58	. . . . 5
10	7, 8, 9	wov 64	. . . 4 $/\$
11	10, 8	weqi 68	. . 3 $/\$
12		weq 38	. . . 4
13	8, 2	weqi 68	. . . . . 6
14	13	id 25	. . . . 5
15	7, 8, 9, 14	oveq1 89	. . . 4 $/\$ $/\$
16	12, 10, 8, 15, 14	oveq12 90	. . 3 $/\$ $/\$
17	7, 2, 9	wov 64	. . . 4 $/\$
18	9, 3	weqi 68	. . . . . 6
19	18	id 25	. . . . 5
20	7, 2, 9, 19	oveq2 91	. . . 4 $/\$ $/\$
21	12, 17, 2, 20	oveq1 89	. . 3 $/\$ $/\$
22	11, 2, 3, 16, 21	ovl 107	. 2 $/\$ $/\$
23	4, 6, 22	eqtri 85	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 109

tim 111

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 df-an 118 df-im 119

This theorem is referenced by: mpd 146 ex 148