Theorem 2exeu 2371

Description: Double existential uniqueness implies double uniqueness quantification. (Contributed by NM, 3-Dec-2001.) (Proof shortened by Mario Carneiro, 22-Dec-2016.)

Assertion

Ref	Expression
2exeu

Proof of Theorem 2exeu

Step	Hyp	Ref	Expression
1		eumo 2313	. . . 4
2		euex 2308	. . . . 5
3	2	moimi 2340	. . . 4
4	1, 3	syl 16	. . 3
5		2euex 2366	. . 3
6	4, 5	anim12ci 567	. 2
7		eu5 2310	. 2
8	6, 7	sylibr 212	1

Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  E!weu 2282  E*wmo 2283

This theorem is referenced by:  2eu1  2376  2eu1OLD  2377  2eu2  2378  2eu3  2379

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-11 1842  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287