This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem e03

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e03.1 ⊢ 𝜑
e03.2 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
e03.3 ⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
Assertion e03 (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e03.1 ⊢ 𝜑
2 e03.2 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
3 e03.3 ⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
4 1 vd03 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜑    )
5 4 2 3 e33 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )