Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > df-riota | GIF version |
Description: Define restricted description binder. In case there is no unique 𝑥 such that (𝑥 ∈ 𝐴 ∧ 𝜑) holds, it evaluates to the empty set. See also comments for df-iota 5136. (Contributed by NM, 15-Sep-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) (Revised by NM, 2-Sep-2018.) |
Ref | Expression |
---|---|
df-riota | ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cA | . . 3 class 𝐴 | |
4 | 1, 2, 3 | crio 5780 | . 2 class (℩𝑥 ∈ 𝐴 𝜑) |
5 | 2 | cv 1334 | . . . . 5 class 𝑥 |
6 | 5, 3 | wcel 2128 | . . . 4 wff 𝑥 ∈ 𝐴 |
7 | 6, 1 | wa 103 | . . 3 wff (𝑥 ∈ 𝐴 ∧ 𝜑) |
8 | 7, 2 | cio 5134 | . 2 class (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) |
9 | 4, 8 | wceq 1335 | 1 wff (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) |
Colors of variables: wff set class |
This definition is referenced by: riotaeqdv 5782 riotabidv 5783 riotaexg 5785 riotav 5786 riotauni 5787 nfriota1 5788 nfriotadxy 5789 cbvriota 5791 riotacl2 5794 riotabidva 5797 riota1 5799 riota2df 5801 snriota 5810 riotaund 5815 bdcriota 13500 |
Copyright terms: Public domain | W3C validator |