Theorem equvinvOLD 1962

Description: Obsolete version of equvinv 1959 as of 11-Apr-2021. (Contributed by NM, 9-Jan-1993.) Remove dependencies on ax-10 2019, ax-13 2246. (Revised by Wolf Lammen, 10-Jun-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equvinvOLD	|- ( x = y <-> E. z ( x = z /\ y = z ) )

Distinct variable groups:   x, z   y, z

Proof of Theorem equvinvOLD

Step	Hyp	Ref	Expression
1		equviniva 1960	. 2 |- ( x = y -> E. z ( x = z /\ y = z ) )
2		equtrr 1949	. . . . 5 |- ( z = y -> ( x = z -> x = y ) )
3	2	equcoms 1947	. . . 4 |- ( y = z -> ( x = z -> x = y ) )
4	3	impcom 446	. . 3 |- ( ( x = z /\ y = z ) -> x = y )
5	4	exlimiv 1858	. 2 |- ( E. z ( x = z /\ y = z ) -> x = y )
6	1, 5	impbii 199	1 |- ( x = y <-> E. z ( x = z /\ y = z ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   E.wex 1704

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)