Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | eqsstr3.1 | ⊢ 𝐵 = 𝐴 | |
| eqsstr3.2 | ⊢ 𝐵 ⊆ 𝐶 | ||
| Assertion | eqsstrri | ⊢ 𝐴 ⊆ 𝐶 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqsstr3.1 | ⊢ 𝐵 = 𝐴 | |
| 2 | eqsstr3.2 | ⊢ 𝐵 ⊆ 𝐶 | |
| 3 | 1 | eqcomi | ⊢ 𝐴 = 𝐵 |
| 4 | 3 2 | eqsstri | ⊢ 𝐴 ⊆ 𝐶 |