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Theorem moel 27155
 Description: "At most one" element in a set. (Contributed by Thierry Arnoux, 26-Jul-2018.)
Assertion
Ref Expression
moel
Distinct variable group:   ,,

Proof of Theorem moel
StepHypRef Expression
1 ralcom4 3132 . 2
2 df-ral 2819 . . 3
32ralbii 2895 . 2
4 alcom 1794 . . 3
5 eleq1 2539 . . . 4
65mo4 2339 . . 3
7 df-ral 2819 . . . . 5
8 impexp 446 . . . . . 6
98albii 1620 . . . . 5
107, 9bitr4i 252 . . . 4
1110albii 1620 . . 3
124, 6, 113bitr4i 277 . 2
131, 3, 123bitr4ri 278 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1377   wceq 1379   wcel 1767  wmo 2276  wral 2814 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-v 3115 This theorem is referenced by:  disjnf  27203
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