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Metamath Proof Explorer

Theorem eqsstri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 16-Jul-1995)

Ref Expression
Hypotheses eqsstr.1 ⊢ A = B
eqsstr.2 ⊢ B ⊆ C
Assertion eqsstri ⊢ A ⊆ C

Proof

Step Hyp Ref Expression
1 eqsstr.1 ⊢ A = B
2 eqsstr.2 ⊢ B ⊆ C
3 1 sseq1i ⊢ A ⊆ C ↔ B ⊆ C
4 2 3 mpbir ⊢ A ⊆ C