Theorem ibib

Description: Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994) (Proof shortened by Wolf Lammen, 24-Jan-2013)

	Ref	Expression
Assertion	ibib	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → ( 𝜑 ↔ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.501	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ↔ 𝜓 ) ) )
2	1	pm5.74i	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → ( 𝜑 ↔ 𝜓 ) ) )