Metamath Proof Explorer


Theorem e31

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e31.1 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
e31.2 (    𝜑    ▶    𝜏    )
e31.3 ( 𝜃 → ( 𝜏𝜂 ) )
Assertion e31 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e31.1 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2 e31.2 (    𝜑    ▶    𝜏    )
3 e31.3 ( 𝜃 → ( 𝜏𝜂 ) )
4 2 vd13 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
5 1 4 3 e33 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )