| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > jaod | Structured version Visualization version GIF version | ||
| Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 18-Aug-1994.) |
| Ref | Expression |
|---|---|
| jaod.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| jaod.2 | ⊢ (𝜑 → (𝜃 → 𝜒)) |
| Ref | Expression |
|---|---|
| jaod | ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jaod.1 | . . . 4 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | 1 | com12 32 | . . 3 ⊢ (𝜓 → (𝜑 → 𝜒)) |
| 3 | jaod.2 | . . . 4 ⊢ (𝜑 → (𝜃 → 𝜒)) | |
| 4 | 3 | com12 32 | . . 3 ⊢ (𝜃 → (𝜑 → 𝜒)) |
| 5 | 2, 4 | jaoi 858 | . 2 ⊢ ((𝜓 ∨ 𝜃) → (𝜑 → 𝜒)) |
| 6 | 5 | com12 32 | 1 ⊢ (𝜑 → ((𝜓 ∨ 𝜃) → 𝜒)) |
| Copyright terms: Public domain | W3C validator |