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Theorem rmo2ilem 2875
 Description: Condition implying restricted "at most one." (Contributed by Jim Kingdon, 14-Jul-2018.)
Hypothesis
Ref Expression
rmo2.1
Assertion
Ref Expression
rmo2ilem
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem rmo2ilem
StepHypRef Expression
1 impexp 254 . . . . 5
21albii 1375 . . . 4
3 df-ral 2328 . . . 4
42, 3bitr4i 180 . . 3
54exbii 1512 . 2
6 nfv 1437 . . . . 5
7 rmo2.1 . . . . 5
86, 7nfan 1473 . . . 4
98mo2r 1968 . . 3
10 df-rmo 2331 . . 3
119, 10sylibr 141 . 2
125, 11sylbir 129 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101  wal 1257   wceq 1259  wnf 1365  wex 1397   wcel 1409  wmo 1917  wral 2323  wrmo 2326 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-ral 2328  df-rmo 2331 This theorem is referenced by:  rmo2i  2876
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