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Metamath Proof Explorer

Theorem eqeltri

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

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

Proof

Step Hyp Ref Expression
1 eqeltri.1 ⊢ A = B
2 eqeltri.2 ⊢ B ∈ C
3 1 eleq1i ⊢ A ∈ C ↔ B ∈ C
4 2 3 mpbir ⊢ A ∈ C