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Metamath Proof Explorer
Description: Theorem 19.22 of Margaris p. 90. (Contributed by NM, 10-Jan-1993)
(Proof shortened by Wolf Lammen, 4-Jul-2014)
|
|
Ref |
Expression |
|
Assertion |
exim |
⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
id |
⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜓 ) ) |
| 2 |
1
|
aleximi |
⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) ) |