Theorem equcomi

Description: Commutative law for equality. Equality is a symmetric relation. Lemma 3 of KalishMontague p. 85. See also Lemma 7 of Tarski p. 69. (Contributed by NM, 10-Jan-1993) (Revised by NM, 9-Apr-2017)

	Ref	Expression
Assertion	equcomi	⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		equid	⊢ 𝑥 = 𝑥
2		ax7	⊢ ( 𝑥 = 𝑦 → ( 𝑥 = 𝑥 → 𝑦 = 𝑥 ) )
3	1 2	mpi	⊢ ( 𝑥 = 𝑦 → 𝑦 = 𝑥 )