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 ) |
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 ) |