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Definition df-cap 32102
Description: Define the little cap function. See brcap 32172 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
StepHypRef Expression
1 ccap 32079 . 2 class Cap
2 cvv 3231 . . . . 5 class V
32, 2cxp 5141 . . . 4 class (V × V)
43, 2cxp 5141 . . 3 class ((V × V) × V)
5 cep 5057 . . . . . 6 class E
62, 5ctxp 32062 . . . . 5 class (V ⊗ E )
7 c1st 7208 . . . . . . . . 9 class 1st
87ccnv 5142 . . . . . . . 8 class 1st
98, 5ccom 5147 . . . . . . 7 class (1st ∘ E )
10 c2nd 7209 . . . . . . . . 9 class 2nd
1110ccnv 5142 . . . . . . . 8 class 2nd
1211, 5ccom 5147 . . . . . . 7 class (2nd ∘ E )
139, 12cin 3606 . . . . . 6 class ((1st ∘ E ) ∩ (2nd ∘ E ))
1413, 2ctxp 32062 . . . . 5 class (((1st ∘ E ) ∩ (2nd ∘ E )) ⊗ V)
156, 14csymdif 3876 . . . 4 class ((V ⊗ E ) △ (((1st ∘ E ) ∩ (2nd ∘ E )) ⊗ V))
1615crn 5144 . . 3 class ran ((V ⊗ E ) △ (((1st ∘ E ) ∩ (2nd ∘ E )) ⊗ V))
174, 16cdif 3604 . 2 class (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((1st ∘ E ) ∩ (2nd ∘ E )) ⊗ V)))
181, 17wceq 1523 1 wff Cap = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (((1st ∘ E ) ∩ (2nd ∘ E )) ⊗ V)))
Colors of variables: wff setvar class
This definition is referenced by:  brcap  32172
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