| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > eqsstrdi | Structured version Visualization version GIF version | ||
| Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017.) |
| Ref | Expression |
|---|---|
| eqsstrdi.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| eqsstrdi.2 | ⊢ 𝐵 ⊆ 𝐶 |
| Ref | Expression |
|---|---|
| eqsstrdi | ⊢ (𝜑 → 𝐴 ⊆ 𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqsstrdi.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | eqsstrdi.2 | . . 3 ⊢ 𝐵 ⊆ 𝐶 | |
| 3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → 𝐵 ⊆ 𝐶) |
| 4 | 1, 3 | eqsstrd 4018 | 1 ⊢ (𝜑 → 𝐴 ⊆ 𝐶) |
| Copyright terms: Public domain | W3C validator |