Metamath Proof Explorer
Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted
quantifier version.) (Contributed by NM, 18-Jun-2014)
|
|
Ref |
Expression |
|
Hypothesis |
ralrimivw.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
ralrimivw |
⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ralrimivw.1 |
⊢ ( 𝜑 → 𝜓 ) |
2 |
1
|
a1d |
⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → 𝜓 ) ) |
3 |
2
|
ralrimiv |
⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 ) |