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Theorem equtr2 1672
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 1671 . . 3  |-  ( z  =  y  ->  (
x  =  z  ->  x  =  y )
)
21equcoms 1669 . 2  |-  ( y  =  z  ->  (
x  =  z  ->  x  =  y )
)
32impcom 124 1  |-  ( ( x  =  z  /\  y  =  z )  ->  x  =  y )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-gen 1410  ax-ie2 1455  ax-8 1467  ax-17 1491  ax-i9 1495
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mo23  2018  euequ1  2072
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