Step |
Hyp |
Ref |
Expression |
0 |
|
cfuns |
⊢ Funs |
1 |
|
cvv |
⊢ V |
2 |
1 1
|
cxp |
⊢ ( V × V ) |
3 |
2
|
cpw |
⊢ 𝒫 ( V × V ) |
4 |
|
cep |
⊢ E |
5 |
|
c1st |
⊢ 1st |
6 |
|
cid |
⊢ I |
7 |
1 6
|
cdif |
⊢ ( V ∖ I ) |
8 |
|
c2nd |
⊢ 2nd |
9 |
7 8
|
ccom |
⊢ ( ( V ∖ I ) ∘ 2nd ) |
10 |
5 9
|
ctxp |
⊢ ( 1st ⊗ ( ( V ∖ I ) ∘ 2nd ) ) |
11 |
4
|
ccnv |
⊢ ◡ E |
12 |
10 11
|
ccom |
⊢ ( ( 1st ⊗ ( ( V ∖ I ) ∘ 2nd ) ) ∘ ◡ E ) |
13 |
4 12
|
ccom |
⊢ ( E ∘ ( ( 1st ⊗ ( ( V ∖ I ) ∘ 2nd ) ) ∘ ◡ E ) ) |
14 |
13
|
cfix |
⊢ Fix ( E ∘ ( ( 1st ⊗ ( ( V ∖ I ) ∘ 2nd ) ) ∘ ◡ E ) ) |
15 |
3 14
|
cdif |
⊢ ( 𝒫 ( V × V ) ∖ Fix ( E ∘ ( ( 1st ⊗ ( ( V ∖ I ) ∘ 2nd ) ) ∘ ◡ E ) ) ) |
16 |
0 15
|
wceq |
⊢ Funs = ( 𝒫 ( V × V ) ∖ Fix ( E ∘ ( ( 1st ⊗ ( ( V ∖ I ) ∘ 2nd ) ) ∘ ◡ E ) ) ) |