Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > anbi2d | GIF version |
Description: Deduction adding a left conjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 16-Nov-2013.) |
Ref | Expression |
---|---|
anbid.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
anbi2d | ⊢ (𝜑 → ((𝜃 ∧ 𝜓) ↔ (𝜃 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anbid.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | 1 | a1d 22 | . 2 ⊢ (𝜑 → (𝜃 → (𝜓 ↔ 𝜒))) |
3 | 2 | pm5.32d 447 | 1 ⊢ (𝜑 → ((𝜃 ∧ 𝜓) ↔ (𝜃 ∧ 𝜒))) |
Copyright terms: Public domain | W3C validator |