Metamath Proof Explorer


Theorem int2

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 is ex . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis int2.1 (    (    𝜑    ,    𝜓    )    ▶    𝜒    )
Assertion int2 (    𝜑    ▶    ( 𝜓𝜒 )    )

Proof

Step Hyp Ref Expression
1 int2.1 (    (    𝜑    ,    𝜓    )    ▶    𝜒    )
2 1 dfvd2ani ( ( 𝜑𝜓 ) → 𝜒 )
3 2 ex ( 𝜑 → ( 𝜓𝜒 ) )
4 3 dfvd1ir (    𝜑    ▶    ( 𝜓𝜒 )    )