This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Inference adding two universal quantifiers to both sides of an
equivalence. (Contributed by NM, 9-Mar-1997)
|
|
Ref |
Expression |
|
Hypothesis |
albii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
Assertion |
2albii |
⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
albii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
| 2 |
1
|
albii |
⊢ ( ∀ 𝑦 𝜑 ↔ ∀ 𝑦 𝜓 ) |
| 3 |
2
|
albii |
⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 𝜓 ) |