Metamath Proof Explorer
Description: Inference form of Theorem 19.21 of Margaris p. 90, see 19.21 .
(Contributed by Mario Carneiro, 24-Sep-2016)
|
|
Ref |
Expression |
|
Hypotheses |
alrimi.1 |
⊢ Ⅎ 𝑥 𝜑 |
|
|
alrimi.2 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
alrimi |
⊢ ( 𝜑 → ∀ 𝑥 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
alrimi.1 |
⊢ Ⅎ 𝑥 𝜑 |
2 |
|
alrimi.2 |
⊢ ( 𝜑 → 𝜓 ) |
3 |
1
|
nf5ri |
⊢ ( 𝜑 → ∀ 𝑥 𝜑 ) |
4 |
3 2
|
alrimih |
⊢ ( 𝜑 → ∀ 𝑥 𝜓 ) |