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Theorem equtrr 1690
Description: A transitive law for equality. Lemma L17 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtrr  |-  ( x  =  y  ->  (
z  =  x  -> 
z  =  y ) )

Proof of Theorem equtrr
StepHypRef Expression
1 equtr 1689 . 2  |-  ( z  =  x  ->  (
x  =  y  -> 
z  =  y ) )
21com12 29 1  |-  ( x  =  y  ->  (
z  =  x  -> 
z  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  equtr2  1695  ax12b  1696  ax12bOLD  1697  ax12OLD  1974  ax12from12o  2190  ax11eq  2227  sbeqalbi  27269  a9e2eq  27987  a9e2eqVD  28360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682
This theorem depends on definitions:  df-bi 178  df-ex 1548
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