Theorem biimp3a

Description: Infer implication from a logical equivalence. Similar to biimpa . (Contributed by NM, 4-Sep-2005)

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

Proof

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