Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | anbi.1 | ⊢ ( 𝜑 ↔ 𝜓 ) | |
| Assertion | anbi2i | ⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜒 ∧ 𝜓 ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anbi.1 | ⊢ ( 𝜑 ↔ 𝜓 ) | |
| 2 | 1 | a1i | ⊢ ( 𝜒 → ( 𝜑 ↔ 𝜓 ) ) |
| 3 | 2 | pm5.32i | ⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜒 ∧ 𝜓 ) ) |