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