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Theorem equcomi 1663
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 1660 . 2  |-  x  =  x
2 ax-8 1465 . 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-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-gen 1408  ax-ie2 1453  ax-8 1465  ax-17 1489  ax-i9 1493
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ax6evr  1664  equcom  1665  equcoms  1667  ax10  1678  cbv2h  1707  equvini  1714  equveli  1715  equsb2  1742  drex1  1752  sbcof2  1764  aev  1766  cbvexdh  1876  rext  4105  iotaval  5067
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