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

Metamath Proof Explorer

Theorem int3

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 is 3expia . (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis int3.1 ⊢ (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    )
Assertion int3 (    (    𝜑    ,    𝜓    )    ▶    ( 𝜒 → 𝜃 )    )

Proof

Step Hyp Ref Expression
1 int3.1 ⊢ (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    )
2 1 dfvd3ani ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
3 2 3expia ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
4 3 dfvd2anir ⊢ (    (    𝜑    ,    𝜓    )    ▶    ( 𝜒 → 𝜃 )    )