Theorem equtr 1653

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 1450	. 2 |- ( y = x -> ( y = z -> x = z ) )
2	1	equcoms 1652	1 |- ( x = y -> ( y = z -> x = z ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-gen 1393  ax-ie2 1438  ax-8 1450  ax-17 1474  ax-i9 1478

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  equtrr  1654  equequ1  1656  equveli  1700  equvin  1802