Metamath Proof Explorer
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 |
Proof
| 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 |