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Theorem rmo2 3423
 Description: Alternate definition of restricted "at most one." Note that is not equivalent to (in analogy to reu6 3288); to see this, let be the empty set. However, one direction of this pattern holds; see rmo2i 3424. (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 2815 . 2
2 nfv 1708 . . . 4
3 rmo2.1 . . . 4
42, 3nfan 1929 . . 3
54mo2 2294 . 2
6 impexp 446 . . . . 5
76albii 1641 . . . 4
8 df-ral 2812 . . . 4
97, 8bitr4i 252 . . 3
109exbii 1668 . 2
111, 5, 103bitri 271 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1393  wex 1613  wnf 1617   wcel 1819  wmo 2284  wral 2807  wrmo 2810 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-nf 1618  df-eu 2287  df-mo 2288  df-ral 2812  df-rmo 2815 This theorem is referenced by:  rmo2i  3424  disjiun  4447  rmoeq  27513  rmoanim  32387
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