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Metamath Proof Explorer
Description: Deduction form of Theorem 19.23 of Margaris p. 90, see 19.23 .
(Contributed by NM, 31-Jul-1995)
|
|
Ref |
Expression |
|
Hypothesis |
exlimdvv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
exlimdvv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
exlimdvv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
1
|
exlimdv |
⊢ ( 𝜑 → ( ∃ 𝑦 𝜓 → 𝜒 ) ) |
| 3 |
2
|
exlimdv |
⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → 𝜒 ) ) |