This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: The range of a restriction is a subset of the whole range. (Contributed by Glauco Siliprandi, 17-Aug-2020)
|
|
Ref |
Expression |
|
Assertion |
rnresss |
⊢ ran ( 𝐴 ↾ 𝐵 ) ⊆ ran 𝐴 |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
resss |
⊢ ( 𝐴 ↾ 𝐵 ) ⊆ 𝐴 |
| 2 |
1
|
rnssi |
⊢ ran ( 𝐴 ↾ 𝐵 ) ⊆ ran 𝐴 |