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Theorem equtr 1694
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)

Proof of Theorem equtr
StepHypRef Expression
1 ax-8 1687 . 2  |-  ( y  =  x  ->  (
y  =  z  ->  x  =  z )
)
21equcoms 1693 1  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  equtrr  1695  equequ1  1696  equveliOLD  2086  equvin  2087  sbequi  2110  axsep  4329  equveliNEW7  29528  equvinNEW7  29529  ax7w9AUX7  29660
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687
This theorem depends on definitions:  df-bi 178  df-ex 1551
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