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Metamath Proof Explorer
Description: Inference adding three universal quantifiers to both sides of an
equivalence. (Contributed by Peter Mazsa, 10-Aug-2018)
|
|
Ref |
Expression |
|
Hypothesis |
albii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
|
Assertion |
3albii |
⊢ ( ∀ 𝑥 ∀ 𝑦 ∀ 𝑧 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 ∀ 𝑧 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
albii.1 |
⊢ ( 𝜑 ↔ 𝜓 ) |
| 2 |
1
|
2albii |
⊢ ( ∀ 𝑦 ∀ 𝑧 𝜑 ↔ ∀ 𝑦 ∀ 𝑧 𝜓 ) |
| 3 |
2
|
albii |
⊢ ( ∀ 𝑥 ∀ 𝑦 ∀ 𝑧 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 ∀ 𝑧 𝜓 ) |