Theorem equtr 1948

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		ax7 1943	. 2 |- ( y = x -> ( y = z -> x = z ) )
2	1	equcoms 1947	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-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  equtrr  1949  equequ1  1952  equviniva  1960  ax6e  2250  equvini  2346  sbequi  2375  axsep  4780  bj-axsep  32793