Metamath Proof Explorer

Theorem ensym

Description: Symmetry of equinumerosity. Theorem 2 of Suppes p. 92. (Contributed by NM, 26-Oct-2003) (Revised by Mario Carneiro, 26-Apr-2015)

Ref Expression
Assertion ensym ( 𝐴 ≈ 𝐵 → 𝐵 ≈ 𝐴 )

Proof

Step Hyp Ref Expression
1 ensymb ⊢ ( 𝐴 ≈ 𝐵 ↔ 𝐵 ≈ 𝐴 )
2 1 biimpi ⊢ ( 𝐴 ≈ 𝐵 → 𝐵 ≈ 𝐴 )