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 )    )