Theorem ancrb 547

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
ancrb	⊢ ((𝜑 → 𝜓) ↔ (𝜑 → (𝜓 ∧ 𝜑)))

Proof of Theorem ancrb

Step	Hyp	Ref	Expression
1		iba 527	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜓 ∧ 𝜑)))
2	1	pm5.74i 270	1 ⊢ ((𝜑 → 𝜓) ↔ (𝜑 → (𝜓 ∧ 𝜑)))

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396

This theorem is referenced by:  rababg  41134