Theorem equcomi 1592

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 1589	. 2 |- x = x
2		ax-8 1395	. 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 99  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-17 1419  ax-i9 1423

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  equcom  1593  equcoms  1594  ax10  1605  cbv2h  1634  equvini  1641  equveli  1642  equsb2  1669  drex1  1679  sbcof2  1691  aev  1693  cbvexdh  1801  rext  3951  iotaval  4878