Theorem vd03

Description: A theorem is virtually inferred by the 3 virtual hypotheses. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	vd03.1	⊢ 𝜑
Assertion	vd03	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜑    )

Proof

Step	Hyp	Ref	Expression
1		vd03.1	⊢ 𝜑
2	1	a1i	⊢ ( 𝜃 → 𝜑 )
3	2	a1i	⊢ ( 𝜒 → ( 𝜃 → 𝜑 ) )
4	3	a1i	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜑 ) ) )
5	4	dfvd3ir	⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜑    )