Theorem bj-bisimpl

Description: Implication from equivalence with a conjunct. Its associated inference is simplbi . (Contributed by BJ, 20-Mar-2026)

	Ref	Expression
Assertion	bj-bisimpl	⊢ ( ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) ) → ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		biimp	⊢ ( ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) ) → ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) )
2		simpl	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜓 )
3	1 2	syl6	⊢ ( ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) ) → ( 𝜑 → 𝜓 ) )