Theorem e21

Description: A virtual deduction elimination rule (see syl6ci ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e21.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e21.2	⊢ (    𝜑    ▶    𝜃    )
	e21.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
Assertion	e21	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e21.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e21.2	⊢ (    𝜑    ▶    𝜃    )
3		e21.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
4	2	vd12	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
5	1 4 3	e22	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )