Theorem e32

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e32.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e32.2	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
	e32.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
Assertion	e32	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e32.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e32.2	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )
3		e32.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
4	2	vd23	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
5	1 4 3	e33	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )