Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > riotav | GIF version |
Description: An iota restricted to the universe is unrestricted. (Contributed by NM, 18-Sep-2011.) |
Ref | Expression |
---|---|
riotav | ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-riota 5468 | . 2 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑)) | |
2 | vex 2560 | . . . 4 ⊢ 𝑥 ∈ V | |
3 | 2 | biantrur 287 | . . 3 ⊢ (𝜑 ↔ (𝑥 ∈ V ∧ 𝜑)) |
4 | 3 | iotabii 4889 | . 2 ⊢ (℩𝑥𝜑) = (℩𝑥(𝑥 ∈ V ∧ 𝜑)) |
5 | 1, 4 | eqtr4i 2063 | 1 ⊢ (℩𝑥 ∈ V 𝜑) = (℩𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 97 = wceq 1243 ∈ wcel 1393 Vcvv 2557 ℩cio 4865 ℩crio 5467 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-uni 3581 df-iota 4867 df-riota 5468 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |