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Theorem rmoimi2 2742
 Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
rmoimi2.1
Assertion
Ref Expression
rmoimi2

Proof of Theorem rmoimi2
StepHypRef Expression
1 rmoimi2.1 . . 3
2 moim 1964 . . 3
31, 2ax-mp 7 . 2
4 df-rmo 2314 . 2
5 df-rmo 2314 . 2
63, 4, 53imtr4i 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241   wcel 1393  wmo 1901  wrmo 2309 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-rmo 2314 This theorem is referenced by: (None)
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