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Theorem nmo 23978
 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 2312 . . 3
32notbii 289 . 2
4 alnex 1553 . 2
5 exnal 1584 . . . 4
6 pm4.61 417 . . . . . 6
7 biid 229 . . . . . . . 8
87necon3bbii 2634 . . . . . . 7
98anbi2i 677 . . . . . 6
106, 9bitri 242 . . . . 5
1110exbii 1593 . . . 4
125, 11bitr3i 244 . . 3
1312albii 1576 . 2
143, 4, 133bitr2i 266 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550  wex 1551  wnf 1554  wmo 2284   wne 2601 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-ne 2603
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