Theorem equtr2OLD 1956

Description: Obsolete proof of equtr2 1954 as of 11-Apr-2021. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equtr2OLD	|- ( ( x = z /\ y = z ) -> x = y )

Proof of Theorem equtr2OLD

Step	Hyp	Ref	Expression
1		equtrr 1949	. . 3 |- ( z = y -> ( x = z -> x = y ) )
2	1	equcoms 1947	. 2 |- ( y = z -> ( x = z -> x = y ) )
3	2	impcom 446	1 |- ( ( x = z /\ y = z ) -> x = y )

Syntax hints:   -> wi 4   /\ wa 384

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: (None)