Metamath Proof Explorer


Theorem e122

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

Ref Expression
Hypotheses e122.1 (    𝜑    ▶    𝜓    )
e122.2 (    𝜑    ,    𝜒    ▶    𝜃    )
e122.3 (    𝜑    ,    𝜒    ▶    𝜏    )
e122.4 ( 𝜓 → ( 𝜃 → ( 𝜏𝜂 ) ) )
Assertion e122 (    𝜑    ,    𝜒    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e122.1 (    𝜑    ▶    𝜓    )
2 e122.2 (    𝜑    ,    𝜒    ▶    𝜃    )
3 e122.3 (    𝜑    ,    𝜒    ▶    𝜏    )
4 e122.4 ( 𝜓 → ( 𝜃 → ( 𝜏𝜂 ) ) )
5 1 vd12 (    𝜑    ,    𝜒    ▶    𝜓    )
6 5 2 3 4 e222 (    𝜑    ,    𝜒    ▶    𝜂    )