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Metamath Proof Explorer

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 )