Theorem ibib 234

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

Assertion

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

Proof of Theorem ibib

Step	Hyp	Ref	Expression
1		pm5.501 233	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 ↔ 𝜓)))
2	1	pm5.74i 169	1 ⊢ ((𝜑 → 𝜓) ↔ (𝜑 → (𝜑 ↔ 𝜓)))

Syntax hints:   → wi 4   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)