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Theorem equtr2 1700
Description: A transitive law for equality. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
equtr2  |-  ( ( x  =  z  /\  y  =  z )  ->  x  =  y )

Proof of Theorem equtr2
StepHypRef Expression
1 equtrr 1695 . . 3  |-  ( z  =  y  ->  (
x  =  z  ->  x  =  y )
)
21equcoms 1693 . 2  |-  ( y  =  z  ->  (
x  =  z  ->  x  =  y )
)
32impcom 420 1  |-  ( ( x  =  z  /\  y  =  z )  ->  x  =  y )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  mo  2303  2mo  2359  euequ1  2369  dchrisumlema  21182  funpartfun  25788
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-an 361  df-ex 1551
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