Description: Introduce a right conjunct to both sides of a logical equivalence. (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | anbi.1 | ⊢ ( 𝜑 ↔ 𝜓 ) | |
| Assertion | anbi1i | ⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anbi.1 | ⊢ ( 𝜑 ↔ 𝜓 ) | |
| 2 | 1 | a1i | ⊢ ( 𝜒 → ( 𝜑 ↔ 𝜓 ) ) |
| 3 | 2 | pm5.32ri | ⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ) ) |