Theorem 2eu2 2378

Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)

Assertion

Ref	Expression
2eu2

Proof of Theorem 2eu2

Step	Hyp	Ref	Expression
1		eumo 2313	. . 3
2		2moex 2365	. . 3
3		2eu1 2376	. . . 4
4		simpl 457	. . . 4
5	3, 4	syl6bi 228	. . 3
6	1, 2, 5	3syl 20	. 2
7		2exeu 2371	. . 3
8	7	expcom 435	. 2
9	6, 8	impbid 191	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:  2eu8  2386

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-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287