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Metamath Proof Explorer

Theorem e13

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

Ref Expression
Hypotheses e13.1 ⊢ (    𝜑    ▶    𝜓    )
e13.2 ⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜏    )
e13.3 ⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
Assertion e13 (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e13.1 ⊢ (    𝜑    ▶    𝜓    )
2 e13.2 ⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜏    )
3 e13.3 ⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
4 1 vd13 ⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜓    )
5 4 2 3 e33 ⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜂    )