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Mirrors > Home > MPE Home > Th. List > nf5dv | Structured version Visualization version GIF version |
Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1710 changed. (Revised by Wolf Lammen, 18-Sep-2021.) |
Ref | Expression |
---|---|
nf5dv.1 | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Ref | Expression |
---|---|
nf5dv | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf5dv.1 | . . 3 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) | |
2 | 1 | alrimiv 1855 | . 2 ⊢ (𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓)) |
3 | nf5-1 2023 | . 2 ⊢ (∀𝑥(𝜓 → ∀𝑥𝜓) → Ⅎ𝑥𝜓) | |
4 | 2, 3 | syl 17 | 1 ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 Ⅎwnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-10 2019 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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