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Theorem equtr2 1679
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 1674 . . 3  |-  ( z  =  y  ->  (
x  =  z  ->  x  =  y )
)
21equcoms 1672 . 2  |-  ( y  =  z  ->  (
x  =  z  ->  x  =  y )
)
32impcom 419 1  |-  ( ( x  =  z  /\  y  =  z )  ->  x  =  y )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  mo  2198  2mo  2254  euequ1  2264  funpartfun  24867
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1533
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