Theorem exsb 2212

Description: An equivalent expression for existence. (Contributed by NM, 2-Feb-2005.)

Assertion

Ref	Expression
exsb

Distinct variable groups:   ,   ,

Proof of Theorem exsb

Step	Hyp	Ref	Expression
1		nfv 1707	. 2
2		nfa1 1897	. 2
3		ax12v 1855	. . 3
4		sp 1859	. . . 4
5	4	com12 31	. . 3
6	3, 5	impbid 191	. 2
7	1, 2, 6	cbvex 2022	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612

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