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Theorem equtrr 1653
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 1652 . 2  |-  ( z  =  x  ->  (
x  =  y  -> 
z  =  y ) )
21com12 27 1  |-  ( x  =  y  ->  (
z  =  x  -> 
z  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  equtr2  1654  ax12b  1655  ax12bOLD  1656  ax12  2095  ax11eq  2132  sbeqalbi  27600  a9e2eq  28323  a9e2eqVD  28683
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
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