Theorem eu3v 2312

Description: An alternate way to express existential uniqueness. (Contributed by NM, 8-Jul-1994.) Add a distinct variable condition on . (Revised by Wolf Lammen, 29-May-2019.)

Assertion

Ref	Expression
eu3v

Distinct variable groups:   ,   ,

Proof of Theorem eu3v

Step	Hyp	Ref	Expression
1		eu5 2310	. 2
2		mo2v 2289	. . 3
3	2	anbi2i 694	. 2
4	1, 3	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  E!weu 2282  E*wmo 2283

This theorem is referenced by:  2eu4OLD  2381  eqeu  3270  reu3  3289  eunex  4645  bj-eunex  34385

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287