Theorem moi2 3280

Description: Consequence of "at most one." (Contributed by NM, 29-Jun-2008.)

Hypothesis

Ref	Expression
moi2.1

Assertion

Ref	Expression
moi2

Distinct variable groups:   ,   ,

Proof of Theorem moi2

Step	Hyp	Ref	Expression
1		moi2.1	. . . . 5
2	1	mob2 3279	. . . 4
3	2	3expa 1196	. . 3
4	3	biimprd 223	. 2
5	4	impr 619	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E*wmo 2283

This theorem is referenced by:  fsum  13542  fprod  13748  txcn  20127  haustsms2  20635

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111