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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nexdvt | Structured version Visualization version GIF version |
Description: Closed form of nexdv 1928. (Contributed by BJ, 20-Oct-2019.) |
Ref | Expression |
---|---|
bj-nexdvt | ⊢ (∀𝑥(𝜑 → ¬ 𝜓) → (𝜑 → ¬ ∃𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1906 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | bj-nexdt 33928 | . 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → ¬ 𝜓) → (𝜑 → ¬ ∃𝑥𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (∀𝑥(𝜑 → ¬ 𝜓) → (𝜑 → ¬ ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1526 ∃wex 1771 Ⅎwnf 1775 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-ex 1772 df-nf 1776 |
This theorem is referenced by: (None) |
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