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Theorem equtrr 1851
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 1850 . 2  |-  ( z  =  x  ->  (
x  =  y  -> 
z  =  y ) )
21com12 32 1  |-  ( x  =  y  ->  (
z  =  x  -> 
z  =  y ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
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-ex 1658
This theorem is referenced by:  equtr2  1856  ax13b  1859  2ax6elem  2248  ax13fromc9  32445  ax12eq  32481  sbeqalbi  36721  ax6e2eq  36894  ax6e2eqVD  37277
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