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Theorem rmo3 3248
 Description: Restricted "at most one" using explicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmo2.1
Assertion
Ref Expression
rmo3
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem rmo3
StepHypRef Expression
1 df-rmo 2713 . 2
2 sban 2139 . . . . . . . . . . 11
3 clelsb3 2538 . . . . . . . . . . . 12
43anbi1i 677 . . . . . . . . . . 11
52, 4bitri 241 . . . . . . . . . 10
65anbi2i 676 . . . . . . . . 9
7 an4 798 . . . . . . . . 9
8 ancom 438 . . . . . . . . . 10
98anbi1i 677 . . . . . . . . 9
106, 7, 93bitri 263 . . . . . . . 8
1110imbi1i 316 . . . . . . 7
12 impexp 434 . . . . . . 7
13 impexp 434 . . . . . . 7
1411, 12, 133bitri 263 . . . . . 6
1514albii 1575 . . . . 5
16 df-ral 2710 . . . . 5
17 r19.21v 2793 . . . . 5
1815, 16, 173bitr2i 265 . . . 4
1918albii 1575 . . 3
20 nfv 1629 . . . . 5
21 rmo2.1 . . . . 5
2220, 21nfan 1846 . . . 4
2322mo3 2312 . . 3
24 df-ral 2710 . . 3
2519, 23, 243bitr4i 269 . 2
261, 25bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553  wsb 1658   wcel 1725  wmo 2282  wral 2705  wrmo 2708 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  ax-ext 2417 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 2285  df-mo 2286  df-cleq 2429  df-clel 2432  df-ral 2710  df-rmo 2713
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