Definition df-cup 31145

Description: Define the little cup function. See brcup 31216 for its value. (Contributed by Scott Fenton, 14-Apr-2014.)

Assertion

Ref	Expression
df-cup	⊢ Cup = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∪ (◡2nd ∘ E )) ⊗ V)))

Detailed syntax breakdown of Definition df-cup

Step	Hyp	Ref	Expression
1		ccup 31122	. 2 class Cup
2		cvv 3173	. . . . 5 class V
3	2, 2	cxp 5036	. . . 4 class (V × V)
4	3, 2	cxp 5036	. . 3 class ((V × V) × V)
5		cep 4947	. . . . . 6 class E
6	2, 5	ctxp 31106	. . . . 5 class (V ⊗ E )
7		c1st 7057	. . . . . . . . 9 class 1st
8	7	ccnv 5037	. . . . . . . 8 class ◡1st
9	8, 5	ccom 5042	. . . . . . 7 class (◡1st ∘ E )
10		c2nd 7058	. . . . . . . . 9 class 2nd
11	10	ccnv 5037	. . . . . . . 8 class ◡2nd
12	11, 5	ccom 5042	. . . . . . 7 class (◡2nd ∘ E )
13	9, 12	cun 3538	. . . . . 6 class ((◡1st ∘ E ) ∪ (◡2nd ∘ E ))
14	13, 2	ctxp 31106	. . . . 5 class (((◡1st ∘ E ) ∪ (◡2nd ∘ E )) ⊗ V)
15	6, 14	csymdif 3805	. . . 4 class ((V ⊗ E ) △ (((◡1st ∘ E ) ∪ (◡2nd ∘ E )) ⊗ V))
16	15	crn 5039	. . 3 class ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∪ (◡2nd ∘ E )) ⊗ V))
17	4, 16	cdif 3537	. 2 class (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∪ (◡2nd ∘ E )) ⊗ V)))
18	1, 17	wceq 1475	1 wff Cup = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((◡1st ∘ E ) ∪ (◡2nd ∘ E )) ⊗ V)))

This definition is referenced by:  brcup  31216