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Definition df-cup 32565
 Description: Define the little cup function. See brcup 32635 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
StepHypRef Expression
1 ccup 32542 . 2 class Cup
2 cvv 3397 . . . . 5 class V
32, 2cxp 5353 . . . 4 class (V × V)
43, 2cxp 5353 . . 3 class ((V × V) × V)
5 cep 5265 . . . . . 6 class E
62, 5ctxp 32526 . . . . 5 class (V ⊗ E )
7 c1st 7443 . . . . . . . . 9 class 1st
87ccnv 5354 . . . . . . . 8 class 1st
98, 5ccom 5359 . . . . . . 7 class (1st ∘ E )
10 c2nd 7444 . . . . . . . . 9 class 2nd
1110ccnv 5354 . . . . . . . 8 class 2nd
1211, 5ccom 5359 . . . . . . 7 class (2nd ∘ E )
139, 12cun 3789 . . . . . 6 class ((1st ∘ E ) ∪ (2nd ∘ E ))
1413, 2ctxp 32526 . . . . 5 class (((1st ∘ E ) ∪ (2nd ∘ E )) ⊗ V)
156, 14csymdif 4065 . . . 4 class ((V ⊗ E ) △ (((1st ∘ E ) ∪ (2nd ∘ E )) ⊗ V))
1615crn 5356 . . 3 class ran ((V ⊗ E ) △ (((1st ∘ E ) ∪ (2nd ∘ E )) ⊗ V))
174, 16cdif 3788 . 2 class (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((1st ∘ E ) ∪ (2nd ∘ E )) ⊗ V)))
181, 17wceq 1601 1 wff Cup = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((1st ∘ E ) ∪ (2nd ∘ E )) ⊗ V)))
 Colors of variables: wff setvar class This definition is referenced by:  brcup  32635
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