Metamath Proof Explorer
Description: Inference form of Theorem 19.21 of Margaris p. 90. See 19.21 and
19.21h . Instance of sylg . (Contributed by NM, 9-Jan-1993)
|
|
Ref |
Expression |
|
Hypotheses |
alrimih.1 |
⊢ ( 𝜑 → ∀ 𝑥 𝜑 ) |
|
|
alrimih.2 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
alrimih |
⊢ ( 𝜑 → ∀ 𝑥 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
alrimih.1 |
⊢ ( 𝜑 → ∀ 𝑥 𝜑 ) |
2 |
|
alrimih.2 |
⊢ ( 𝜑 → 𝜓 ) |
3 |
1 2
|
sylg |
⊢ ( 𝜑 → ∀ 𝑥 𝜓 ) |