Step |
Hyp |
Ref |
Expression |
0 |
|
cR |
|- R |
1 |
|
cA |
|- A |
2 |
|
cX |
|- X |
3 |
1 0 2
|
ctrpred |
|- TrPred ( R , A , X ) |
4 |
|
va |
|- a |
5 |
|
cvv |
|- _V |
6 |
|
vy |
|- y |
7 |
4
|
cv |
|- a |
8 |
6
|
cv |
|- y |
9 |
1 0 8
|
cpred |
|- Pred ( R , A , y ) |
10 |
6 7 9
|
ciun |
|- U_ y e. a Pred ( R , A , y ) |
11 |
4 5 10
|
cmpt |
|- ( a e. _V |-> U_ y e. a Pred ( R , A , y ) ) |
12 |
1 0 2
|
cpred |
|- Pred ( R , A , X ) |
13 |
11 12
|
crdg |
|- rec ( ( a e. _V |-> U_ y e. a Pred ( R , A , y ) ) , Pred ( R , A , X ) ) |
14 |
|
com |
|- _om |
15 |
13 14
|
cres |
|- ( rec ( ( a e. _V |-> U_ y e. a Pred ( R , A , y ) ) , Pred ( R , A , X ) ) |` _om ) |
16 |
15
|
crn |
|- ran ( rec ( ( a e. _V |-> U_ y e. a Pred ( R , A , y ) ) , Pred ( R , A , X ) ) |` _om ) |
17 |
16
|
cuni |
|- U. ran ( rec ( ( a e. _V |-> U_ y e. a Pred ( R , A , y ) ) , Pred ( R , A , X ) ) |` _om ) |
18 |
3 17
|
wceq |
|- TrPred ( R , A , X ) = U. ran ( rec ( ( a e. _V |-> U_ y e. a Pred ( R , A , y ) ) , Pred ( R , A , X ) ) |` _om ) |