Theorem equcomi 1632

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 1629	. 2 |- x = x
2		ax-8 1435	. 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 1378  ax-ie2 1423  ax-8 1435  ax-17 1459  ax-i9 1463

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  equcom  1633  equcoms  1634  ax10  1645  cbv2h  1674  equvini  1681  equveli  1682  equsb2  1709  drex1  1719  sbcof2  1731  aev  1733  cbvexdh  1842  rext  3970  iotaval  4898