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Mirrors > Home > NFE Home > Th. List > df-pm | Unicode version |
Description: Define the partial mapping operation. A partial function from to is a function from a subset of to . The set of all partial functions from to is written (see pmvalg 6010). A notation for this operation apparently does not appear in the literature. We use to distinguish it from the less general set exponentiation operation (df-map 6001) . See mapsspm 6021 for its relationship to set exponentiation. (Contributed by NM, 15-Nov-2007.) |
Ref | Expression |
---|---|
df-pm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpm 6000 | . 2 | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cvv 2859 | . . 3 | |
5 | vf | . . . . . 6 | |
6 | 5 | cv 1641 | . . . . 5 |
7 | 6 | wfun 4775 | . . . 4 |
8 | 3 | cv 1641 | . . . . . 6 |
9 | 2 | cv 1641 | . . . . . 6 |
10 | 8, 9 | cxp 4770 | . . . . 5 |
11 | 10 | cpw 3722 | . . . 4 |
12 | 7, 5, 11 | crab 2618 | . . 3 |
13 | 2, 3, 4, 4, 12 | cmpt2 5653 | . 2 |
14 | 1, 13 | wceq 1642 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: fnpm 6008 pmvalg 6010 |
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