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Metamath Proof Explorer

Theorem e12

Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e12.1 ⊢ (    𝜑    ▶    𝜓    )
e12.2 ⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
e12.3 ⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
Assertion e12 (    𝜑    ,    𝜒    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e12.1 ⊢ (    𝜑    ▶    𝜓    )
2 e12.2 ⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
3 e12.3 ⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
4 1 vd12 ⊢ (    𝜑    ,    𝜒    ▶    𝜓    )
5 4 2 3 e22 ⊢ (    𝜑    ,    𝜒    ▶    𝜏    )