Theorem ggen22

Description: gen22 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ggen22.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	ggen22	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		ggen22.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	alrimdv	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑦 𝜒 ) )
3	2	alrimdv	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )