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Metamath Proof Explorer
Description: Inference quantifying antecedent, nested antecedent, and consequent.
(Contributed by NM, 10-Jan-1993)
|
|
Ref |
Expression |
|
Hypothesis |
al2imi.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
al2imi |
⊢ ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
al2imi.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
|
al2im |
⊢ ( ∀ 𝑥 ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) ) ) |
| 3 |
2 1
|
mpg |
⊢ ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) ) |