Theorem equtr 1723

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

Step	Hyp	Ref	Expression
1		ax-8 1518	. 2 |- ( y = x -> ( y = z -> x = z ) )
2	1	equcoms 1722	1 |- ( x = y -> ( y = z -> x = z ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-gen 1463  ax-ie2 1508  ax-8 1518  ax-17 1540  ax-i9 1544

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  equtrr  1724  equequ1  1726  equveli  1773  equvin  1877