Theorem dfvd3ani

Description: Inference form of dfvd3an . (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfvd3ani.1	⊢ (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    )
Assertion	dfvd3ani	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		dfvd3ani.1	⊢ (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    )
2		dfvd3an	⊢ ( (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) )
3	1 2	mpbi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )