Metamath Proof Explorer


Theorem e200

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

Ref Expression
Hypotheses e200.1 (    𝜑    ,    𝜓    ▶    𝜒    )
e200.2 𝜃
e200.3 𝜏
e200.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
Assertion e200 (    𝜑    ,    𝜓    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e200.1 (    𝜑    ,    𝜓    ▶    𝜒    )
2 e200.2 𝜃
3 e200.3 𝜏
4 e200.4 ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 2 vd02 (    𝜑    ,    𝜓    ▶    𝜃    )
6 3 vd02 (    𝜑    ,    𝜓    ▶    𝜏    )
7 1 5 6 4 e222 (    𝜑    ,    𝜓    ▶    𝜂    )