MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  equtrr Unicode version

Theorem equtrr 1654
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 1653 . 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  1655  ax12b  1656  ax12bOLD  1657  ax12  2097  ax11eq  2133  sbeqalbi  27011  a9e2eq  27606  a9e2eqVD  27963
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 1636  ax-8 1644
  Copyright terms: Public domain W3C validator