Metamath Proof Explorer
Description: Inference quantifying both antecedent and consequent, with strong
hypothesis. (Contributed by NM, 4-Mar-1997)
|
|
Ref |
Expression |
|
Hypothesis |
ralimi.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
ralimi |
⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ralimi.1 |
⊢ ( 𝜑 → 𝜓 ) |
2 |
1
|
a1i |
⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) ) |
3 |
2
|
ralimia |
⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 ) |