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Metamath Proof Explorer

Theorem gen12

Description: Virtual deduction generalizing rule for two quantifying variables and one virtual hypothesis. gen12 is alrimivv with virtual deductions. (Contributed by Alan Sare, 2-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	gen12.1	⊢ ( 𝜑 ▶ 𝜓 )
	Assertion	gen12	⊢ ( 𝜑 ▶ ∀ 𝑥 ∀ 𝑦 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		gen12.1	⊢ ( 𝜑 ▶ 𝜓 )
2	1	in1	⊢ ( 𝜑 → 𝜓 )
3	2	alrimivv	⊢ ( 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 )
4	3	dfvd1ir	⊢ ( 𝜑 ▶ ∀ 𝑥 ∀ 𝑦 𝜓 )