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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfdt | Structured version Visualization version GIF version |
Description: Closed form of nf5d 2118 and nf5dh 2026. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-nfdt | ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → Ⅎ𝑥𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nfdt0 32685 | . 2 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓)) | |
2 | 1 | imim2d 57 | 1 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → ((𝜑 → ∀𝑥𝜑) → (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-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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