Definition df-cap 33326

Description: Define the little cap function. See brcap 33396 for its value. (Contributed by Scott Fenton, 17-Apr-2014.)

Assertion

Ref	Expression
df-cap	⊢ Cap = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∩ (◡2nd ∘ E )) ⊗ V)))

Detailed syntax breakdown of Definition df-cap

Step	Hyp	Ref	Expression
1		ccap 33303	. 2 class Cap
2		cvv 3494	. . . . 5 class V
3	2, 2	cxp 5547	. . . 4 class (V × V)
4	3, 2	cxp 5547	. . 3 class ((V × V) × V)
5		cep 5458	. . . . . 6 class E
6	2, 5	ctxp 33286	. . . . 5 class (V ⊗ E )
7		c1st 7681	. . . . . . . . 9 class 1st
8	7	ccnv 5548	. . . . . . . 8 class ◡1st
9	8, 5	ccom 5553	. . . . . . 7 class (◡1st ∘ E )
10		c2nd 7682	. . . . . . . . 9 class 2nd
11	10	ccnv 5548	. . . . . . . 8 class ◡2nd
12	11, 5	ccom 5553	. . . . . . 7 class (◡2nd ∘ E )
13	9, 12	cin 3934	. . . . . 6 class ((◡1st ∘ E ) ∩ (◡2nd ∘ E ))
14	13, 2	ctxp 33286	. . . . 5 class (((◡1st ∘ E ) ∩ (◡2nd ∘ E )) ⊗ V)
15	6, 14	csymdif 4217	. . . 4 class ((V ⊗ E ) △ (((◡1st ∘ E ) ∩ (◡2nd ∘ E )) ⊗ V))
16	15	crn 5550	. . 3 class ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∩ (◡2nd ∘ E )) ⊗ V))
17	4, 16	cdif 3932	. 2 class (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∩ (◡2nd ∘ E )) ⊗ V)))
18	1, 17	wceq 1533	1 wff Cap = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∩ (◡2nd ∘ E )) ⊗ V)))

This definition is referenced by:  brcap  33396