Theorem n0moeu 3798

Description: A case of equivalence of "at most one" and "only one". (Contributed by FL, 6-Dec-2010.)

Assertion

Ref	Expression
n0moeu

Distinct variable group:   ,

Proof of Theorem n0moeu

Step	Hyp	Ref	Expression
1		n0 3794	. . . 4
2	1	biimpi 194	. . 3
3	2	biantrurd 508	. 2
4		eu5 2310	. 2
5	3, 4	syl6bbr 263	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  E!weu 2282  E*wmo 2283  =/=wne 2652  c0 3784

This theorem is referenced by:  minveclem4a  21845  frg2wot1  25057

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-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-ne 2654  df-v 3111  df-dif 3478  df-nul 3785