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Theorem rmo2 3131
 Description: Alternate definition of restricted "at most one." Note that is not equivalent to (in analogy to reu6 3025); to see this, let be the empty set. However, one direction of this pattern holds; see rmo2i 3132. (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 2622 . 2
2 nfv 1619 . . . 4
3 rmo2.1 . . . 4
42, 3nfan 1824 . . 3
54mo2 2233 . 2
6 impexp 433 . . . . 5
76albii 1566 . . . 4
8 df-ral 2619 . . . 4
97, 8bitr4i 243 . . 3
109exbii 1582 . 2
111, 5, 103bitri 262 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541  wnf 1544   wcel 1710  wmo 2205  wral 2614  wrmo 2617 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-ral 2619  df-rmo 2622 This theorem is referenced by:  rmo2i  3132
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