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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 1408 | . 2 ⊢ (Ⅎxψ → (ψ → ∀xψ)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (φ → (ψ → ∀xψ)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1240 Ⅎwnf 1346 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-4 1397 |
This theorem depends on definitions: df-bi 110 df-nf 1347 |
This theorem is referenced by: nfan1 1453 nfim1 1460 alrimdd 1497 spimed 1625 cbv2 1632 nfald 1640 sbied 1668 cbvexd 1799 sbcomxyyz 1843 hbsbd 1855 dvelimALT 1883 dvelimfv 1884 hbeud 1919 abidnf 2703 eusvnfb 4152 |
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