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Theorem equcomi 1589
Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equcomi (x = yy = x)

Proof of Theorem equcomi
StepHypRef Expression
1 equid 1586 . 2 x = x
2 ax-8 1392 . 2 (x = y → (x = xy = x))
31, 2mpi 15 1 (x = yy = 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 99  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-17 1416  ax-i9 1420
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  equcom  1590  equcoms  1591  ax10  1602  cbv2h  1631  equvini  1638  equveli  1639  equsb2  1666  drex1  1676  sbcof2  1688  aev  1690  cbvexdh  1798  rext  3942  iotaval  4821
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