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Definition df-funs 31137
Description: Define the class of all functions. See elfuns 31192 for membership. (Contributed by Scott Fenton, 18-Feb-2013.)
Assertion
Ref Expression
df-funs Funs = (𝒫 (V × V) ∖ Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )))

Detailed syntax breakdown of Definition df-funs
StepHypRef Expression
1 cfuns 31113 . 2 class Funs
2 cvv 3173 . . . . 5 class V
32, 2cxp 5036 . . . 4 class (V × V)
43cpw 4108 . . 3 class 𝒫 (V × V)
5 cep 4947 . . . . 5 class E
6 c1st 7057 . . . . . . 7 class 1st
7 cid 4948 . . . . . . . . 9 class I
82, 7cdif 3537 . . . . . . . 8 class (V ∖ I )
9 c2nd 7058 . . . . . . . 8 class 2nd
108, 9ccom 5042 . . . . . . 7 class ((V ∖ I ) ∘ 2nd )
116, 10ctxp 31106 . . . . . 6 class (1st ⊗ ((V ∖ I ) ∘ 2nd ))
125ccnv 5037 . . . . . 6 class E
1311, 12ccom 5042 . . . . 5 class ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )
145, 13ccom 5042 . . . 4 class ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E ))
1514cfix 31111 . . 3 class Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E ))
164, 15cdif 3537 . 2 class (𝒫 (V × V) ∖ Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )))
171, 16wceq 1475 1 wff Funs = (𝒫 (V × V) ∖ Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )))
Colors of variables: wff setvar class
This definition is referenced by:  elfuns  31192
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