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Theorem equcomi 1574
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 1571 . 2 x = x
2 ax-8 1376 . 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 1318  ax-ie2 1364  ax-8 1376  ax-17 1400  ax-i9 1404
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  equcom  1575  equcoms  1576  ax10  1587  cbv2h  1616  equvini  1623  equveli  1624  equsb2  1651  drex1  1661  sbcof2  1673  aev  1675  cbvexdh  1783  rext  3925  iotaval  4805
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