Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mo5f Structured version   Unicode version

Theorem mo5f 23962
 Description: Alternate definition of "at most one." (Contributed by Thierry Arnoux, 1-Mar-2017.)
Hypotheses
Ref Expression
mo5f.1
mo5f.2
Assertion
Ref Expression
mo5f
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem mo5f
StepHypRef Expression
1 mo5f.2 . . 3
21mo3 2311 . 2
3 mo5f.1 . . . . . 6
43nfsb 2184 . . . . . 6
53, 4nfan 1846 . . . . 5
6 nfv 1629 . . . . 5
75, 6nfim 1832 . . . 4
87nfal 1864 . . 3
98sb8 2167 . 2
10 sbim 2121 . . . . 5
11 sban 2143 . . . . . . 7
12 nfs1v 2181 . . . . . . . . . 10
1312sbf 2105 . . . . . . . . 9
1413bicomi 194 . . . . . . . 8
1514anbi2i 676 . . . . . . 7
1611, 15bitr4i 244 . . . . . 6
17 equsb3 2177 . . . . . 6
1816, 17imbi12i 317 . . . . 5
1910, 18bitri 241 . . . 4
2019sbalv 2205 . . 3
2120albii 1575 . 2
222, 9, 213bitri 263 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553  wsb 1658  wmo 2281 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285
 Copyright terms: Public domain W3C validator