Higher-Order Logic Explorer		< Previous   Next > Nearby theorems
Mirrors  >  Home  >  HOLE Home  >  Th. List  >  exlimdv		Unicode version

---

Theorem exlimdv 157

Description: Existential elimination.

Hypothesis

Ref	Expression
exlimdv.1

Assertion

Ref	Expression
exlimdv

Distinct variable groups:   ,   ,   ,

---

Proof of Theorem exlimdv Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		exlimdv.1	. . . . 5
2	1	ax-cb1 29	. . . 4
3	2	wctr 32	. . 3
4	3	wl 59	. 2
5		wv 58	. . . 4
6	4, 5	wc 45	. . 3
7	1	ax-cb2 30	. . 3
8		wim 127	. . . . 5
9	8, 6, 7	wov 64	. . . 4
10	1	ex 148	. . . 4
11		wv 58	. . . . 5
12	8, 11	ax-17 95	. . . . 5
13	3, 11	ax-hbl1 93	. . . . . 6
14	5, 11	ax-17 95	. . . . . 6
15	4, 5, 11, 13, 14	hbc 100	. . . . 5
16	7, 11	ax-17 95	. . . . 5
17	8, 6, 11, 7, 12, 15, 16	hbov 101	. . . 4
18		wv 58	. . . . . . . 8
19	18, 5	weqi 68	. . . . . . 7
20	4, 18	wc 45	. . . . . . . 8
21	3	beta 82	. . . . . . . 8
22	20, 21	eqcomi 70	. . . . . . 7
23	19, 22	a1i 28	. . . . . 6
24	19	id 25	. . . . . . 7
25	4, 18, 24	ceq2 80	. . . . . 6
26	3, 23, 25	eqtri 85	. . . . 5
27	8, 3, 7, 26	oveq1 89	. . . 4
28	5, 9, 10, 17, 27	insti 104	. . 3
29	6, 7, 28	imp 147	. 2
30	4, 29	exlimdv2 156	1

Colors of variables: type var term

Syntax hints:  tv 1   ht 2  hb 3  kc 5  kl 6   ke 7  kt 8  kbr 9  kct 10   wffMMJ2 11   tim 111  tex 113

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-ded 43  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-al 116  df-an 118  df-im 119  df-ex 121

This theorem is referenced by: (None)

Copyright terms: Public domain

W3C validator