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Mirrors > Home > ILE 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 6521). 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 6512) . See mapsspm 6544 for its relationship to set exponentiation. (Contributed by NM, 15-Nov-2007.) |
Ref | Expression |
---|---|
df-pm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpm 6511 | . 2 | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cvv 2660 | . . 3 | |
5 | vf | . . . . . 6 | |
6 | 5 | cv 1315 | . . . . 5 |
7 | 6 | wfun 5087 | . . . 4 |
8 | 3 | cv 1315 | . . . . . 6 |
9 | 2 | cv 1315 | . . . . . 6 |
10 | 8, 9 | cxp 4507 | . . . . 5 |
11 | 10 | cpw 3480 | . . . 4 |
12 | 7, 5, 11 | crab 2397 | . . 3 |
13 | 2, 3, 4, 4, 12 | cmpo 5744 | . 2 |
14 | 1, 13 | wceq 1316 | 1 |
Colors of variables: wff set class |
This definition is referenced by: fnpm 6518 pmvalg 6521 elpmi 6529 pmresg 6538 pmsspw 6545 |
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