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Metamath Proof Explorer

Theorem e20

Description: A virtual deduction elimination rule (see syl6mpi ). (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e20.1 ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
e20.2 ⊢ 𝜃
e20.3 ⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
Assertion e20 (    𝜑    ,    𝜓    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e20.1 ⊢ (    𝜑    ,    𝜓    ▶    𝜒    )
2 e20.2 ⊢ 𝜃
3 e20.3 ⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
4 2 vd02 ⊢ (    𝜑    ,    𝜓    ▶    𝜃    )
5 1 4 3 e22 ⊢ (    𝜑    ,    𝜓    ▶    𝜏    )