Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfreuxy | GIF version |
Description: Not-free for restricted uniqueness. This is a version where 𝑥 and 𝑦 are distinct. (Contributed by Jim Kingdon, 6-Jun-2018.) |
Ref | Expression |
---|---|
nfreuxy.1 | ⊢ Ⅎ𝑥𝐴 |
nfreuxy.2 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfreuxy | ⊢ Ⅎ𝑥∃!𝑦 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1355 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfreuxy.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
4 | nfreuxy.2 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
5 | 4 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
6 | 1, 3, 5 | nfreudxy 2483 | . 2 ⊢ (⊤ → Ⅎ𝑥∃!𝑦 ∈ 𝐴 𝜑) |
7 | 6 | trud 1252 | 1 ⊢ Ⅎ𝑥∃!𝑦 ∈ 𝐴 𝜑 |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1244 Ⅎwnf 1349 Ⅎwnfc 2165 ∃!wreu 2308 |
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-eu 1903 df-cleq 2033 df-clel 2036 df-nfc 2167 df-reu 2313 |
This theorem is referenced by: sbcreug 2838 |
Copyright terms: Public domain | W3C validator |