Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfcrd | GIF version |
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfeqd.1 | ⊢ (𝜑 → Ⅎ𝑥𝐴) |
Ref | Expression |
---|---|
nfcrd | ⊢ (𝜑 → Ⅎ𝑥 𝑦 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeqd.1 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝐴) | |
2 | nfcr 2211 | . 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → Ⅎ𝑥 𝑦 ∈ 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1389 ∈ wcel 1433 Ⅎwnfc 2206 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-4 1440 |
This theorem depends on definitions: df-bi 115 df-nfc 2208 |
This theorem is referenced by: nfeqd 2233 nfeld 2234 dvelimdc 2238 nfcsbd 2939 nfifd 3376 |
Copyright terms: Public domain | W3C validator |