Theorem equcomi 1661

Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem equcomi

Step	Hyp	Ref	Expression
1		equid 1658	. 2 ⊢ 𝑥 = 𝑥
2		ax-8 1463	. 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑥 → 𝑦 = 𝑥))
3	1, 2	mpi 15	1 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-gen 1406  ax-ie2 1451  ax-8 1463  ax-17 1487  ax-i9 1491

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ax6evr  1662  equcom  1663  equcoms  1665  ax10  1676  cbv2h  1705  equvini  1712  equveli  1713  equsb2  1740  drex1  1750  sbcof2  1762  aev  1764  cbvexdh  1874  rext  4095  iotaval  5055