![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nexdvt | Structured version Visualization version GIF version |
Description: Closed form of nexdv 1940. (Contributed by BJ, 20-Oct-2019.) |
Ref | Expression |
---|---|
bj-nexdvt | ⊢ (∀𝑥(𝜑 → ¬ 𝜓) → (𝜑 → ¬ ∃𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1918 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | bj-nexdt 35191 | . 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 1540 ∃wex 1782 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-12 2172 |
This theorem depends on definitions: df-bi 206 df-ex 1783 df-nf 1787 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |