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Metamath Proof Explorer

Theorem e102

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e102.1 ⊢ (    𝜑    ▶    𝜓    )
e102.2 ⊢ 𝜒
e102.3 ⊢ (    𝜑    ,    𝜃    ▶    𝜏    )
e102.4 ⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
Assertion e102 (    𝜑    ,    𝜃    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e102.1 ⊢ (    𝜑    ▶    𝜓    )
2 e102.2 ⊢ 𝜒
3 e102.3 ⊢ (    𝜑    ,    𝜃    ▶    𝜏    )
4 e102.4 ⊢ ( 𝜓 → ( 𝜒 → ( 𝜏 → 𝜂 ) ) )
5 2 vd01 ⊢ (    𝜑    ▶    𝜒    )
6 1 5 3 4 e112 ⊢ (    𝜑    ,    𝜃    ▶    𝜂    )