Theorem equtr2 1639

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 1638	. . 3 |- ( z = y -> ( x = z -> x = y ) )
2	1	equcoms 1636	. 2 |- ( y = z -> ( x = z -> x = y ) )
3	2	impcom 123	1 |- ( ( x = z /\ y = z ) -> x = y )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  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:  mo23  1984  euequ1  2038