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Metamath Proof Explorer
Theorem sps
Description: Generalization of antecedent. (Contributed by NM, 5-Jan-1993)
|
|
Ref |
Expression |
|
Hypothesis |
sps.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
sps |
⊢ ( ∀ 𝑥 𝜑 → 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
sps.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
|
sp |
⊢ ( ∀ 𝑥 𝜑 → 𝜑 ) |
| 3 |
2 1
|
syl |
⊢ ( ∀ 𝑥 𝜑 → 𝜓 ) |