Theorem equvinivOLD 1961

Description: The forward implication of equvinv 1959. Obsolete as of 11-Apr-2021. Use equvinv 1959 instead. (Contributed by Wolf Lammen, 11-Apr-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Distinct variable groups:   x, z   y, z

Proof of Theorem equvinivOLD

Step	Hyp	Ref	Expression
1		ax6ev 1890	. 2 |- E. z z = x
2		equtrr 1949	. . . 4 |- ( x = y -> ( z = x -> z = y ) )
3	2	ancld 576	. . 3 |- ( x = y -> ( z = x -> ( z = x /\ z = y ) ) )
4	3	eximdv 1846	. 2 |- ( x = y -> ( E. z z = x -> E. z ( z = x /\ z = y ) ) )
5	1, 4	mpi 20	1 |- ( x = y -> E. z ( z = x /\ z = y ) )

Syntax hints:   -> wi 4   /\ 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)