Metamath Proof Explorer


Theorem equcom

Description: Commutative law for equality. Equality is a symmetric relation. (Contributed by NM, 20-Aug-1993)

Ref Expression
Assertion equcom ( 𝑥 = 𝑦 ↔ 𝑦 = 𝑥 )

Proof

Step Hyp Ref Expression
1 equcomi ⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )
2 equcomi ⊢ ( 𝑦 = 𝑥 → 𝑥 = 𝑦 )
3 1 2 impbii ⊢ ( 𝑥 = 𝑦 ↔ 𝑦 = 𝑥 )