Theorem equtr2 1711

Description: A transitive law for equality. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)

Assertion

Ref	Expression
equtr2	|- ( ( x = z /\ y = z ) -> x = y )

Proof of Theorem equtr2

Step	Hyp	Ref	Expression
1		equtrr 1710	. . 3 |- ( z = y -> ( x = z -> x = y ) )
2	1	equcoms 1708	. 2 |- ( y = z -> ( x = z -> x = y ) )
3	2	impcom 125	1 |- ( ( x = z /\ y = z ) -> x = y )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-gen 1449  ax-ie2 1494  ax-8 1504  ax-17 1526  ax-i9 1530

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  mo23  2067  euequ1  2121