Theorem dfvd2anir

Description: Right-to-left inference form of dfvd2an . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfvd2anir.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	dfvd2anir	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜒    )

Proof

Step	Hyp	Ref	Expression
1		dfvd2anir.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		dfvd2an	⊢ ( (    (    𝜑    ,    𝜓    )    ▶    𝜒    ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
3	1 2	mpbir	⊢ (    (    𝜑    ,    𝜓    )    ▶    𝜒    )