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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 1483 | . 2 ⊢ (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1314 Ⅎwnf 1421 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-4 1472 |
This theorem depends on definitions: df-bi 116 df-nf 1422 |
This theorem is referenced by: nfan1 1528 nfim1 1535 alrimdd 1573 spimed 1703 cbv2 1710 nfald 1718 sbied 1746 cbvexd 1879 sbcomxyyz 1923 hbsbd 1935 dvelimALT 1963 dvelimfv 1964 hbeud 1999 abidnf 2825 eusvnfb 4345 |
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