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Theorem nmo 28121
 Description: Negation of "at most one". (Contributed by Thierry Arnoux, 26-Feb-2017.)
Hypothesis
Ref Expression
nmo.1
Assertion
Ref Expression
nmo
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem nmo
StepHypRef Expression
1 nmo.1 . . . 4
21mo2 2308 . . 3
32notbii 298 . 2
4 alnex 1665 . 2
5 exnal 1699 . . . 4
6 pm4.61 428 . . . . . 6
7 biid 240 . . . . . . . 8
87necon3bbii 2671 . . . . . . 7
98anbi2i 700 . . . . . 6
106, 9bitri 253 . . . . 5
1110exbii 1718 . . . 4
125, 11bitr3i 255 . . 3
1312albii 1691 . 2
143, 4, 133bitr2i 277 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1442  wex 1663  wnf 1667  wmo 2300   wne 2622 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668  df-eu 2303  df-mo 2304  df-ne 2624 This theorem is referenced by: (None)
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