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Metamath Proof Explorer

Theorem eqeltrri

Description: Substitution of equal classes into membership relation. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses eqeltrri.1 ⊢ A = B
eqeltrri.2 ⊢ A ∈ C
Assertion eqeltrri ⊢ B ∈ C

Proof

Step Hyp Ref Expression
1 eqeltrri.1 ⊢ A = B
2 eqeltrri.2 ⊢ A ∈ C
3 1 eqcomi ⊢ B = A
4 3 2 eqeltri ⊢ B ∈ C