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

Metamath Proof Explorer

Theorem e23

Description: A virtual deduction elimination rule (see syl10 ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e23.1 ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
e23.2 ⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜏    )
e23.3 ⊢ ( 𝜒 → ( 𝜏 → 𝜂 ) )
Assertion e23 (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e23.1 ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2 e23.2 ⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜏    )
3 e23.3 ⊢ ( 𝜒 → ( 𝜏 → 𝜂 ) )
4 1 vd23 ⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜒    )
5 4 2 3 e33 ⊢ (    𝜑    ,    𝜓    ,    𝜃    ▶    𝜂    )