Theorem ancrb 322

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 300	. 2 ⊢ (𝜑 → (𝜓 ↔ (𝜓 ∧ 𝜑)))
2	1	pm5.74i 180	1 ⊢ ((𝜑 → 𝜓) ↔ (𝜑 → (𝜓 ∧ 𝜑)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104   ↔ wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by: (None)