Metamath Proof Explorer


Definition df-img

Description: Define the image function. See brimg for its value. (Contributed by Scott Fenton, 12-Apr-2014)

Ref Expression
Assertion df-img Img = ( Image ( ( 2nd ∘ 1st ) ↾ ( 1st ↾ ( V × V ) ) ) ∘ Cart )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cimg Img
1 c2nd 2nd
2 c1st 1st
3 1 2 ccom ( 2nd ∘ 1st )
4 cvv V
5 4 4 cxp ( V × V )
6 2 5 cres ( 1st ↾ ( V × V ) )
7 3 6 cres ( ( 2nd ∘ 1st ) ↾ ( 1st ↾ ( V × V ) ) )
8 7 cimage Image ( ( 2nd ∘ 1st ) ↾ ( 1st ↾ ( V × V ) ) )
9 ccart Cart
10 8 9 ccom ( Image ( ( 2nd ∘ 1st ) ↾ ( 1st ↾ ( V × V ) ) ) ∘ Cart )
11 0 10 wceq Img = ( Image ( ( 2nd ∘ 1st ) ↾ ( 1st ↾ ( V × V ) ) ) ∘ Cart )