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Definition df-cart 31946
Description: Define the cartesian product function. See brcart 32014 for its value. (Contributed by Scott Fenton, 11-Apr-2014.)
Assertion
Ref Expression
df-cart Cart = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (pprod( E , E ) ⊗ V)))

Detailed syntax breakdown of Definition df-cart
StepHypRef Expression
1 ccart 31922 . 2 class Cart
2 cvv 3195 . . . . 5 class V
32, 2cxp 5102 . . . 4 class (V × V)
43, 2cxp 5102 . . 3 class ((V × V) × V)
5 cep 5018 . . . . . 6 class E
62, 5ctxp 31911 . . . . 5 class (V ⊗ E )
75, 5cpprod 31912 . . . . . 6 class pprod( E , E )
87, 2ctxp 31911 . . . . 5 class (pprod( E , E ) ⊗ V)
96, 8csymdif 3835 . . . 4 class ((V ⊗ E ) △ (pprod( E , E ) ⊗ V))
109crn 5105 . . 3 class ran ((V ⊗ E ) △ (pprod( E , E ) ⊗ V))
114, 10cdif 3564 . 2 class (((V × V) × V) ∖ ran ((V ⊗ E ) △ (pprod( E , E ) ⊗ V)))
121, 11wceq 1481 1 wff Cart = (((V × V) × V) ∖ ran ((V ⊗ E ) △ (pprod( E , E ) ⊗ V)))
Colors of variables: wff setvar class
This definition is referenced by:  brcart  32014
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