Theorem e2

Description: A virtual deduction elimination rule. syl6 is e2 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e2.2	⊢ ( 𝜒 → 𝜃 )
Assertion	e2	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )

Proof

Step	Hyp	Ref	Expression
1		e2.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e2.2	⊢ ( 𝜒 → 𝜃 )
3	1	dfvd2i	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	3 2	syl6	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
5	4	dfvd2ir	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )