Metamath Proof Explorer


Theorem in2an

Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. expd is the non-virtual deduction form of in2an . (Contributed by Alan Sare, 30-Jun-2012) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis in2an.1 (    𝜑    ,    ( 𝜓𝜒 )    ▶    𝜃    )
Assertion in2an (    𝜑    ,    𝜓    ▶    ( 𝜒𝜃 )    )

Proof

Step Hyp Ref Expression
1 in2an.1 (    𝜑    ,    ( 𝜓𝜒 )    ▶    𝜃    )
2 1 dfvd2i ( 𝜑 → ( ( 𝜓𝜒 ) → 𝜃 ) )
3 2 expd ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
4 3 dfvd2ir (    𝜑    ,    𝜓    ▶    ( 𝜒𝜃 )    )