Theorem e12

Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e12.1	⊢ (    𝜑    ▶    𝜓    )
	e12.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
	e12.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
Assertion	e12	⊢ (    𝜑    ,    𝜒    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e12.1	⊢ (    𝜑    ▶    𝜓    )
2		e12.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
3		e12.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
4	1	vd12	⊢ (    𝜑    ,    𝜒    ▶    𝜓    )
5	4 2 3	e22	⊢ (    𝜑    ,    𝜒    ▶    𝜏    )