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Metamath Proof Explorer
Description: Nested unique existential quantifier and at-most-one quantifier.
(Contributed by NM, 3-Dec-2001)
|
|
Ref |
Expression |
|
Assertion |
2eumo |
⊢ ( ∃! 𝑥 ∃* 𝑦 𝜑 → ∃* 𝑥 ∃! 𝑦 𝜑 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
euimmo |
⊢ ( ∀ 𝑥 ( ∃! 𝑦 𝜑 → ∃* 𝑦 𝜑 ) → ( ∃! 𝑥 ∃* 𝑦 𝜑 → ∃* 𝑥 ∃! 𝑦 𝜑 ) ) |
| 2 |
|
eumo |
⊢ ( ∃! 𝑦 𝜑 → ∃* 𝑦 𝜑 ) |
| 3 |
1 2
|
mpg |
⊢ ( ∃! 𝑥 ∃* 𝑦 𝜑 → ∃* 𝑥 ∃! 𝑦 𝜑 ) |