Definition df-eu 133

Description: Define the 'exists unique' operator. (Contributed by Mario Carneiro, 8-Oct-2014.)

Assertion

Ref	Expression
df-eu	|- T. |= [E! = \p:(al -> *) (E.\y:al (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]]))]

Distinct variable group:   x,p,y

Detailed syntax breakdown of Definition df-eu

Step	Hyp	Ref	Expression
1		kt 8	. 2 term T.
2		teu 125	. . 3 term E!
3		hal	. . . . 5 type al
4		hb 3	. . . . 5 type *
5	3, 4	ht 2	. . . 4 type (al -> *)
6		vp	. . . 4 var p
7		tex 123	. . . . 5 term E.
8		vy	. . . . . 6 var y
9		tal 122	. . . . . . 7 term A.
10		vx	. . . . . . . 8 var x
11	5, 6	tv 1	. . . . . . . . . 10 term p:(al -> *)
12	3, 10	tv 1	. . . . . . . . . 10 term x:al
13	11, 12	kc 5	. . . . . . . . 9 term (p:(al -> *)x:al)
14	3, 8	tv 1	. . . . . . . . . 10 term y:al
15		ke 7	. . . . . . . . . 10 term =
16	12, 14, 15	kbr 9	. . . . . . . . 9 term [x:al = y:al]
17	13, 16, 15	kbr 9	. . . . . . . 8 term [(p:(al -> *)x:al) = [x:al = y:al]]
18	3, 10, 17	kl 6	. . . . . . 7 term \x:al [(p:(al -> *)x:al) = [x:al = y:al]]
19	9, 18	kc 5	. . . . . 6 term (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]])
20	3, 8, 19	kl 6	. . . . 5 term \y:al (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]])
21	7, 20	kc 5	. . . 4 term (E.\y:al (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]]))
22	5, 6, 21	kl 6	. . 3 term \p:(al -> *) (E.\y:al (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]]))
23	2, 22, 15	kbr 9	. 2 term [E! = \p:(al -> *) (E.\y:al (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]]))]
24	1, 23	wffMMJ2 11	1 wff T. |= [E! = \p:(al -> *) (E.\y:al (A.\x:al [(p:(al -> *)x:al) = [x:al = y:al]]))]

This definition is referenced by:  weu  141  euval  144