Theorem equcomi 1635

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 1632	. 2 ⊢ 𝑥 = 𝑥
2		ax-8 1438	. 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 104  ax-gen 1381  ax-ie2 1426  ax-8 1438  ax-17 1462  ax-i9 1466

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  ax6evr  1636  equcom  1637  equcoms  1638  ax10  1649  cbv2h  1678  equvini  1685  equveli  1686  equsb2  1713  drex1  1723  sbcof2  1735  aev  1737  cbvexdh  1846  rext  4016  iotaval  4957