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Metamath Proof Explorer
Description: Inference adding two existential quantifiers to antecedent and
consequent. (Contributed by NM, 3-Feb-2005)
|
|
Ref |
Expression |
|
Hypothesis |
eximi.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
2eximi |
⊢ ( ∃ 𝑥 ∃ 𝑦 𝜑 → ∃ 𝑥 ∃ 𝑦 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
eximi.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
1
|
eximi |
⊢ ( ∃ 𝑦 𝜑 → ∃ 𝑦 𝜓 ) |
| 3 |
2
|
eximi |
⊢ ( ∃ 𝑥 ∃ 𝑦 𝜑 → ∃ 𝑥 ∃ 𝑦 𝜓 ) |