Theorem gen22

Description: Virtual deduction generalizing rule for two quantifying variables and two virtual hypothesis. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	gen22.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
Assertion	gen22	⊢ (    𝜑    ,    𝜓    ▶    ∀ 𝑥 ∀ 𝑦 𝜒    )

Proof

Step	Hyp	Ref	Expression
1		gen22.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2	1	dfvd2i	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	alrimdv	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑦 𝜒 ) )
4	3	alrimdv	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 ∀ 𝑦 𝜒 ) )
5	4	dfvd2ir	⊢ (    𝜑    ,    𝜓    ▶    ∀ 𝑥 ∀ 𝑦 𝜒    )