Theorem biimp3ar

Description: Infer implication from a logical equivalence. Similar to biimpar . (Contributed by NM, 2-Jan-2009)

	Ref	Expression
Hypothesis	biimp3a.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
Assertion	biimp3ar	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		biimp3a.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
2	1	exbiri	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )
3	2	3imp	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜒 )