Theorem e121

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e121.1	⊢ (    𝜑    ▶    𝜓    )
	e121.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
	e121.3	⊢ (    𝜑    ▶    𝜏    )
	e121.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e121	⊢ (    𝜑    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e121.1	⊢ (    𝜑    ▶    𝜓    )
2		e121.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
3		e121.3	⊢ (    𝜑    ▶    𝜏    )
4		e121.4	⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	vd12	⊢ (    𝜑    ,    𝜒    ▶    𝜓    )
6	3	vd12	⊢ (    𝜑    ,    𝜒    ▶    𝜏    )
7	5 2 6 4	e222	⊢ (    𝜑    ,    𝜒    ▶    𝜂    )