Theorem vd23

Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	vd23.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
Assertion	vd23	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜒    )

Proof

Step	Hyp	Ref	Expression
1		vd23.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2	1	dfvd2i	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	a1dd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )
4	3	dfvd3ir	⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜒    )