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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfdt0 | Structured version Visualization version GIF version |
Description: A theorem close to a closed form of nf5d 2280 and nf5dh 2143. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-nfdt0 | ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alim 1812 | . 2 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → ∀𝑥(𝜓 → ∀𝑥𝜓))) | |
2 | nf5 2278 | . 2 ⊢ (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl6ibr 251 | 1 ⊢ (∀𝑥(𝜑 → (𝜓 → ∀𝑥𝜓)) → (∀𝑥𝜑 → Ⅎ𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1539 Ⅎwnf 1785 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-10 2137 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-or 846 df-ex 1782 df-nf 1786 |
This theorem is referenced by: bj-nfdt 35161 |
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