ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  equcomi GIF version

Theorem equcomi 1608
Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equcomi (𝑥 = 𝑦𝑦 = 𝑥)

Proof of Theorem equcomi
StepHypRef Expression
1 equid 1605 . 2 𝑥 = 𝑥
2 ax-8 1411 . 2 (𝑥 = 𝑦 → (𝑥 = 𝑥𝑦 = 𝑥))
31, 2mpi 15 1 (𝑥 = 𝑦𝑦 = 𝑥)
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-gen 1354  ax-ie2 1399  ax-8 1411  ax-17 1435  ax-i9 1439
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  equcom  1609  equcoms  1610  ax10  1621  cbv2h  1650  equvini  1657  equveli  1658  equsb2  1685  drex1  1695  sbcof2  1707  aev  1709  cbvexdh  1817  rext  3979  iotaval  4906
  Copyright terms: Public domain W3C validator