Theorem 19.21bbi

Description: Inference removing two universal quantifiers. Version of 19.21bi with two quantifiers. (Contributed by NM, 20-Apr-1994)

	Ref	Expression
Hypothesis	19.21bbi.1	⊢ ( 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 )
Assertion	19.21bbi	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		19.21bbi.1	⊢ ( 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 )
2	1	19.21bi	⊢ ( 𝜑 → ∀ 𝑦 𝜓 )
3	2	19.21bi	⊢ ( 𝜑 → 𝜓 )