Metamath Proof Explorer


Theorem idn3

Description: Virtual deduction identity rule for three virtual hypotheses. (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion idn3 (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜒    )

Proof

Step Hyp Ref Expression
1 idd ( 𝜓 → ( 𝜒𝜒 ) )
2 1 a1i ( 𝜑 → ( 𝜓 → ( 𝜒𝜒 ) ) )
3 2 dfvd3ir (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜒    )