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Theorem equtr2 1856
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 1851 . . 3  |-  ( z  =  y  ->  (
x  =  z  ->  x  =  y )
)
21equcoms 1849 . 2  |-  ( y  =  z  ->  (
x  =  z  ->  x  =  y )
)
32impcom 431 1  |-  ( ( x  =  z  /\  y  =  z )  ->  x  =  y )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658
This theorem is referenced by:  nfeqf  2104  mo3  2306  madurid  19667  dchrisumlema  24324  funpartfun  30715  bj-mo3OLD  31417  wl-mo3t  31869  fundmge2nop  38889
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