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Metamath Proof Explorer
Description: A closed version of 19.9h . (Contributed by NM, 13-May-1993) (Proof
shortened by Wolf Lammen, 3-Mar-2018)
|
|
Ref |
Expression |
|
Assertion |
19.9ht |
⊢ ( ∀ 𝑥 ( 𝜑 → ∀ 𝑥 𝜑 ) → ( ∃ 𝑥 𝜑 → 𝜑 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
nf5-1 |
⊢ ( ∀ 𝑥 ( 𝜑 → ∀ 𝑥 𝜑 ) → Ⅎ 𝑥 𝜑 ) |
| 2 |
1
|
19.9d |
⊢ ( ∀ 𝑥 ( 𝜑 → ∀ 𝑥 𝜑 ) → ( ∃ 𝑥 𝜑 → 𝜑 ) ) |