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Theorem equtrr 1827
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 1826 . 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 6
This theorem is referenced by:  equtr2  1828  equequ2  1830  ax12b  1834  ax12  1882  ax11eq  2109  sbeqalbi  26968  a9e2eq  27459  a9e2eqVD  27816
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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