Metamath Proof Explorer


Theorem el0321old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses el0321old.1 𝜑
el0321old.2 (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜏    )
el0321old.3 ( ( 𝜑𝜏 ) → 𝜂 )
Assertion el0321old (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 el0321old.1 𝜑
2 el0321old.2 (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜏    )
3 el0321old.3 ( ( 𝜑𝜏 ) → 𝜂 )
4 2 dfvd3ani ( ( 𝜓𝜒𝜃 ) → 𝜏 )
5 1 4 3 eel0321old ( ( 𝜓𝜒𝜃 ) → 𝜂 )
6 5 dfvd3anir (    (    𝜓    ,    𝜒    ,    𝜃    )    ▶    𝜂    )