Metamath Proof Explorer


Theorem ancrb

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

Ref Expression
Assertion ancrb ( ( 𝜑𝜓 ) ↔ ( 𝜑 → ( 𝜓𝜑 ) ) )

Proof

Step Hyp Ref Expression
1 iba ( 𝜑 → ( 𝜓 ↔ ( 𝜓𝜑 ) ) )
2 1 pm5.74i ( ( 𝜑𝜓 ) ↔ ( 𝜑 → ( 𝜓𝜑 ) ) )