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Metamath Proof Explorer
Description: Deduction form of Theorem 19.22 of Margaris p. 90 with two
quantifiers, see exim . (Contributed by NM, 3-Aug-1995)
|
|
Ref |
Expression |
|
Hypothesis |
2alimdv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
2eximdv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → ∃ 𝑥 ∃ 𝑦 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
2alimdv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
1
|
eximdv |
⊢ ( 𝜑 → ( ∃ 𝑦 𝜓 → ∃ 𝑦 𝜒 ) ) |
| 3 |
2
|
eximdv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → ∃ 𝑥 ∃ 𝑦 𝜒 ) ) |