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Metamath Proof Explorer

Theorem gen21

Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 is alrimdv with virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	gen21.1	$⊢ (φ, ψ \to χ)$
	Assertion	gen21	$⊢ (φ, ψ \to \forall x χ)$

Proof

Step	Hyp	Ref	Expression
1		gen21.1	$⊢ (φ, ψ \to χ)$
2	1	dfvd2i	$⊢ φ \to (ψ \to χ)$
3	2	alrimdv	$⊢ φ \to (ψ \to \forall x χ)$
4	3	dfvd2ir	$⊢ (φ, ψ \to \forall x χ)$