Theorem equcomi 1680

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 1677	. 2 ⊢ 𝑥 = 𝑥
2		ax-8 1482	. 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-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-gen 1425  ax-ie2 1470  ax-8 1482  ax-17 1506  ax-i9 1510

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ax6evr  1681  equcom  1682  equcoms  1684  ax10  1695  cbv2h  1724  equvini  1731  equveli  1732  equsb2  1759  drex1  1770  sbcof2  1782  aev  1784  cbvexdh  1898  rext  4137  iotaval  5099  prodmodc  11347