Theorem e20

Description: A virtual deduction elimination rule (see syl6mpi ). (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e20.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e20.2	⊢ 𝜃
	e20.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
Assertion	e20	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e20.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e20.2	⊢ 𝜃
3		e20.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
4	2	vd02	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
5	1 4 3	e22	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )