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Theorem rmo3f 2852
 Description: Restricted "at most one" using explicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.) (Revised by Thierry Arnoux, 8-Oct-2017.)
Hypotheses
Ref Expression
rmo3f.1
rmo3f.2
rmo3f.3
Assertion
Ref Expression
rmo3f
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem rmo3f
StepHypRef Expression
1 df-rmo 2399 . 2
2 sban 1904 . . . . . . . . . . 11
3 rmo3f.1 . . . . . . . . . . . . 13
43clelsb3f 2260 . . . . . . . . . . . 12
54anbi1i 451 . . . . . . . . . . 11
62, 5bitri 183 . . . . . . . . . 10
76anbi2i 450 . . . . . . . . 9
8 an4 558 . . . . . . . . 9
9 ancom 264 . . . . . . . . . 10
109anbi1i 451 . . . . . . . . 9
117, 8, 103bitri 205 . . . . . . . 8
1211imbi1i 237 . . . . . . 7
13 impexp 261 . . . . . . 7
14 impexp 261 . . . . . . 7
1512, 13, 143bitri 205 . . . . . 6
1615albii 1429 . . . . 5
17 df-ral 2396 . . . . 5
18 rmo3f.2 . . . . . . 7
1918nfcri 2250 . . . . . 6
2019r19.21 2483 . . . . 5
2116, 17, 203bitr2i 207 . . . 4
2221albii 1429 . . 3
23 rmo3f.3 . . . . 5
2419, 23nfan 1527 . . . 4
2524mo3 2029 . . 3
26 df-ral 2396 . . 3
2722, 25, 263bitr4i 211 . 2
281, 27bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1312  wnf 1419   wcel 1463  wsb 1718  wmo 1976  wnfc 2243  wral 2391  wrmo 2394 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rmo 2399 This theorem is referenced by:  rmo4f  2853
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