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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 1411 | . 2 ⊢ (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1241 Ⅎwnf 1349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-4 1400 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: nfan1 1456 nfim1 1463 alrimdd 1500 spimed 1628 cbv2 1635 nfald 1643 sbied 1671 cbvexd 1802 sbcomxyyz 1846 hbsbd 1858 dvelimALT 1886 dvelimfv 1887 hbeud 1922 abidnf 2709 eusvnfb 4186 |
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