![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > nfsab | GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfsab.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfsab | ⊢ Ⅎ𝑥 𝑧 ∈ {𝑦 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfsab.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nfri 1519 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | 2 | hbab 2168 | . 2 ⊢ (𝑧 ∈ {𝑦 ∣ 𝜑} → ∀𝑥 𝑧 ∈ {𝑦 ∣ 𝜑}) |
4 | 3 | nfi 1462 | 1 ⊢ Ⅎ𝑥 𝑧 ∈ {𝑦 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1460 ∈ wcel 2148 {cab 2163 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 |
This theorem is referenced by: nfab 2324 peano2 4594 |
Copyright terms: Public domain | W3C validator |