Theorem 2mos 2375

Description: Double "exists at most one", using implicit substitution. (Contributed by NM, 10-Feb-2005.)

Hypothesis

Ref	Expression
2mos.1

Assertion

Ref	Expression
2mos

Distinct variable groups:   ,,   ,,   ,,,

Proof of Theorem 2mos

Step	Hyp	Ref	Expression
1		2mo 2373	. 2
2		nfv 1707	. . . . . . 7
3		2mos.1	. . . . . . . 8
4	3	sbiedv 2152	. . . . . . 7
5	2, 4	sbie 2149	. . . . . 6
6	5	anbi2i 694	. . . . 5
7	6	imbi1i 325	. . . 4
8	7	2albii 1641	. . 3
9	8	2albii 1641	. 2
10	1, 9	bitri 249	1

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

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-sb 1740  df-eu 2286  df-mo 2287