Theorem equcomi 1633

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 1630	. 2 |- x = x
2		ax-8 1436	. 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 1379  ax-ie2 1424  ax-8 1436  ax-17 1460  ax-i9 1464

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  equcom  1634  equcoms  1635  ax10  1646  cbv2h  1675  equvini  1682  equveli  1683  equsb2  1710  drex1  1720  sbcof2  1732  aev  1734  cbvexdh  1843  rext  3978  iotaval  4908