Description: Equality implies equivalence of membership. (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 20-Nov-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | eleq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ∈ 𝐴 ↔ 𝐶 ∈ 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | ⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 ) | |
2 | 1 | eleq2d | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ∈ 𝐴 ↔ 𝐶 ∈ 𝐵 ) ) |