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Theorem equtrr 1695
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 1694 . 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  1700  ax12b  1701  ax12bOLD  1702  ax12OLD  2020  sbequi  2136  ax12from12o  2232  ax11eq  2269  sbeqalbi  27558  a9e2eq  28571  a9e2eqVD  28946
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-ex 1551
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