Metamath Proof Explorer
Description: Generalization rule for restricted quantification. (Contributed by NM, 19-Nov-1994)
|
|
Ref |
Expression |
|
Hypothesis |
rgen.1 |
⊢ ( 𝑥 ∈ 𝐴 → 𝜑 ) |
|
Assertion |
rgen |
⊢ ∀ 𝑥 ∈ 𝐴 𝜑 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
rgen.1 |
⊢ ( 𝑥 ∈ 𝐴 → 𝜑 ) |
2 |
|
df-ral |
⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 ↔ ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 ) ) |
3 |
2 1
|
mpgbir |
⊢ ∀ 𝑥 ∈ 𝐴 𝜑 |