This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Double quantification with "at most one". (Contributed by NM, 3-Dec-2001)
|
|
Ref |
Expression |
|
Assertion |
2moexv |
⊢ ( ∃* 𝑥 ∃ 𝑦 𝜑 → ∀ 𝑦 ∃* 𝑥 𝜑 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
nfe1 |
⊢ Ⅎ 𝑦 ∃ 𝑦 𝜑 |
| 2 |
1
|
nfmov |
⊢ Ⅎ 𝑦 ∃* 𝑥 ∃ 𝑦 𝜑 |
| 3 |
|
19.8a |
⊢ ( 𝜑 → ∃ 𝑦 𝜑 ) |
| 4 |
3
|
moimi |
⊢ ( ∃* 𝑥 ∃ 𝑦 𝜑 → ∃* 𝑥 𝜑 ) |
| 5 |
2 4
|
alrimi |
⊢ ( ∃* 𝑥 ∃ 𝑦 𝜑 → ∀ 𝑦 ∃* 𝑥 𝜑 ) |