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Definition df-funs 35827
Description: Define the class of all functions. See elfuns 35881 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 35803 . 2 class Funs
2 cvv 3488 . . . . 5 class V
32, 2cxp 5698 . . . 4 class (V × V)
43cpw 4622 . . 3 class 𝒫 (V × V)
5 cep 5598 . . . . 5 class E
6 c1st 8030 . . . . . . 7 class 1st
7 cid 5592 . . . . . . . . 9 class I
82, 7cdif 3973 . . . . . . . 8 class (V ∖ I )
9 c2nd 8031 . . . . . . . 8 class 2nd
108, 9ccom 5704 . . . . . . 7 class ((V ∖ I ) ∘ 2nd )
116, 10ctxp 35796 . . . . . 6 class (1st ⊗ ((V ∖ I ) ∘ 2nd ))
125ccnv 5699 . . . . . 6 class E
1311, 12ccom 5704 . . . . 5 class ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )
145, 13ccom 5704 . . . 4 class ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E ))
1514cfix 35801 . . 3 class Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E ))
164, 15cdif 3973 . 2 class (𝒫 (V × V) ∖ Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )))
171, 16wceq 1537 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  35881
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