| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > anim1ci | Structured version Visualization version GIF version | ||
| Description: Introduce conjunct to both sides of an implication. (Contributed by Peter Mazsa, 24-Sep-2022.) |
| Ref | Expression |
|---|---|
| anim1i.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| anim1ci | ⊢ ((𝜑 ∧ 𝜒) → (𝜒 ∧ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anim1i.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | id 22 | . 2 ⊢ (𝜒 → 𝜒) | |
| 3 | 1, 2 | anim12ci 614 | 1 ⊢ ((𝜑 ∧ 𝜒) → (𝜒 ∧ 𝜓)) |
| Copyright terms: Public domain | W3C validator |