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Metamath Proof Explorer
Description: Inference adding existential quantifier to antecedent and consequent.
(Contributed by NM, 10-Jan-1993)
|
|
Ref |
Expression |
|
Hypothesis |
eximi.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
eximi |
⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
eximi.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
|
exim |
⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) ) |
| 3 |
2 1
|
mpg |
⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) |