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Metamath Proof Explorer
Description: Deduction form of Theorem 19.20 of Margaris p. 90 with two
quantifiers, see alim . (Contributed by NM, 27-Apr-2004)
|
|
Ref |
Expression |
|
Hypothesis |
2alimdv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
2alimdv |
⊢ ( 𝜑 → ( ∀ 𝑥 ∀ 𝑦 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
2alimdv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
1
|
alimdv |
⊢ ( 𝜑 → ( ∀ 𝑦 𝜓 → ∀ 𝑦 𝜒 ) ) |
| 3 |
2
|
alimdv |
⊢ ( 𝜑 → ( ∀ 𝑥 ∀ 𝑦 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) ) |