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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
StepHypRef Expression
1 equid 1630 . 2  |-  x  =  x
2 ax-8 1436 . 2  |-  ( x  =  y  ->  (
x  =  x  -> 
y  =  x ) )
31, 2mpi 15 1  |-  ( x  =  y  ->  y  =  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 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
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