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Theorem equcomi 1637
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 1634 . 2  |-  x  =  x
2 ax-8 1440 . 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 1383  ax-ie2 1428  ax-8 1440  ax-17 1464  ax-i9 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ax6evr  1638  equcom  1639  equcoms  1641  ax10  1652  cbv2h  1681  equvini  1688  equveli  1689  equsb2  1716  drex1  1726  sbcof2  1738  aev  1740  cbvexdh  1849  rext  4033  iotaval  4978
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