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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 1451 | . 2 ⊢ (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1282 Ⅎwnf 1389 |
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-nf 1390 |
This theorem is referenced by: nfan1 1496 nfim1 1503 alrimdd 1540 spimed 1668 cbv2 1675 nfald 1683 sbied 1711 cbvexd 1843 sbcomxyyz 1887 hbsbd 1899 dvelimALT 1927 dvelimfv 1928 hbeud 1963 abidnf 2760 eusvnfb 4204 |
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