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