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Metamath Proof Explorer
Description: Inference adding universal quantifier to both sides of an equivalence.
(Contributed by NM, 7-Aug-1994)
|
|
Ref |
Expression |
|
Hypothesis |
albii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
Assertion |
albii |
⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
albii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
| 2 |
|
albi |
⊢ ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) → ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 ) ) |
| 3 |
2 1
|
mpg |
⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜓 ) |