Theorem equcomi 1681

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 1678	. 2 |- x = x
2		ax-8 1483	. 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 1426  ax-ie2 1471  ax-8 1483  ax-17 1507  ax-i9 1511

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  ax6evr  1682  equcom  1683  equcoms  1685  ax10  1696  cbv2h  1725  equvini  1732  equveli  1733  equsb2  1760  drex1  1771  sbcof2  1783  aev  1785  cbvexdh  1899  rext  4145  iotaval  5107  prodmodc  11379