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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 ) |