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Definition df-funs 32298
Description: Define the class of all functions. See elfuns 32352 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 32274 . 2 class Funs
2 cvv 3351 . . . . 5 class V
32, 2cxp 5247 . . . 4 class (V × V)
43cpw 4297 . . 3 class 𝒫 (V × V)
5 cep 5161 . . . . 5 class E
6 c1st 7311 . . . . . . 7 class 1st
7 cid 5156 . . . . . . . . 9 class I
82, 7cdif 3720 . . . . . . . 8 class (V ∖ I )
9 c2nd 7312 . . . . . . . 8 class 2nd
108, 9ccom 5253 . . . . . . 7 class ((V ∖ I ) ∘ 2nd )
116, 10ctxp 32267 . . . . . 6 class (1st ⊗ ((V ∖ I ) ∘ 2nd ))
125ccnv 5248 . . . . . 6 class E
1311, 12ccom 5253 . . . . 5 class ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )
145, 13ccom 5253 . . . 4 class ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E ))
1514cfix 32272 . . 3 class Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E ))
164, 15cdif 3720 . 2 class (𝒫 (V × V) ∖ Fix ( E ∘ ((1st ⊗ ((V ∖ I ) ∘ 2nd )) ∘ E )))
171, 16wceq 1631 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  32352
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