This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem vd13

Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and a two additional hypotheses. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis vd13.1 ⊢ (    𝜑    ▶    𝜓    )
Assertion vd13 (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜓    )

Proof

Step Hyp Ref Expression
1 vd13.1 ⊢ (    𝜑    ▶    𝜓    )
2 1 in1 ⊢ ( 𝜑 → 𝜓 )
3 2 a1d ⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )
4 3 a1dd ⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜓 ) ) )
5 4 dfvd3ir ⊢ (    𝜑    ,    𝜒    ,    𝜃    ▶    𝜓    )