Theorem 2exsb 2213

Description: An equivalent expression for double existence. (Contributed by NM, 2-Feb-2005.) (Proof shortened by Wolf Lammen, 30-Sep-2018.)

Assertion

Ref	Expression
2exsb

Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem 2exsb

Step	Hyp	Ref	Expression
1		2sb8e 2211	. 2
2		2sb6 2188	. . 3
3	2	2exbii 1668	. 2
4	1, 3	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  [wsb 1739

This theorem is referenced by:  2moOLD  2374  2eu6  2383  2eu6OLD  2384

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-ex 1613  df-nf 1617  df-sb 1740