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 )