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Theorem rmo2 3238
 Description: Alternate definition of restricted "at most one." Note that is not equivalent to (in analogy to reu6 3115); to see this, let be the empty set. However, one direction of this pattern holds; see rmo2i 3239. (Contributed by NM, 17-Jun-2017.)
Hypothesis
Ref Expression
rmo2.1
Assertion
Ref Expression
rmo2
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem rmo2
StepHypRef Expression
1 df-rmo 2705 . 2
2 nfv 1629 . . . 4
3 rmo2.1 . . . 4
42, 3nfan 1846 . . 3
54mo2 2309 . 2
6 impexp 434 . . . . 5
76albii 1575 . . . 4
8 df-ral 2702 . . . 4
97, 8bitr4i 244 . . 3
109exbii 1592 . 2
111, 5, 103bitri 263 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  wnf 1553   wcel 1725  wmo 2281  wral 2697  wrmo 2700 This theorem is referenced by:  rmo2i  3239  disjiun  4194  rmoanim  27924 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-ral 2702  df-rmo 2705
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