Theorem bj-ax6elem2 32652

Description: Lemma for bj-ax6e 32653. (Contributed by BJ, 22-Dec-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ax6elem2	|- ( A. x y = z -> E. x x = y )

Distinct variable group:   x, z

Proof of Theorem bj-ax6elem2

Step	Hyp	Ref	Expression
1		ax6ev 1890	. . 3 |- E. x x = z
2		equeucl 1951	. . 3 |- ( x = z -> ( y = z -> x = y ) )
3	1, 2	eximii 1764	. 2 |- E. x ( y = z -> x = y )
4	3	19.35i 1806	1 |- ( A. x y = z -> E. x x = y )

Syntax hints:   -> wi 4   A.wal 1481   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:  bj-ax6e  32653