Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfrd | GIF version |
Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfrd.1 | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Ref | Expression |
---|---|
nfrd | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfrd.1 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜓) | |
2 | nfr 1498 | . 2 ⊢ (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1329 Ⅎwnf 1436 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-4 1487 |
This theorem depends on definitions: df-bi 116 df-nf 1437 |
This theorem is referenced by: nfan1 1543 nfim1 1550 alrimdd 1588 spimed 1718 cbv2 1725 nfald 1733 sbied 1761 cbvexd 1899 sbcomxyyz 1945 hbsbd 1957 dvelimALT 1985 dvelimfv 1986 hbeud 2021 abidnf 2852 eusvnfb 4375 |
Copyright terms: Public domain | W3C validator |