Theorem e22

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e22.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
	e22.2	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
	e22.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
Assertion	e22	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e22.1	⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2		e22.2	⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
3		e22.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
4	3	a1i	⊢ ( 𝜒 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5	1 1 2 4	e222	⊢ (    𝜑    ,    𝜓    ▶    𝜏    )