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Metamath Proof Explorer

Theorem eqsstrri

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