ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  equtr Unicode version

Theorem equtr 1637
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)

Proof of Theorem equtr
StepHypRef Expression
1 ax-8 1436 . 2  |-  ( y  =  x  ->  (
y  =  z  ->  x  =  z )
)
21equcoms 1636 1  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-gen 1379  ax-ie2 1424  ax-8 1436  ax-17 1460  ax-i9 1464
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  equtrr  1638  equequ1  1640  equveli  1684  equvin  1786
  Copyright terms: Public domain W3C validator