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Theorem rmo3 2970
 Description: Restricted at-most-one quantifier 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 2399 . 2
2 sban 1904 . . . . . . . . . . 11
3 clelsb3 2220 . . . . . . . . . . . 12
43anbi1i 451 . . . . . . . . . . 11
52, 4bitri 183 . . . . . . . . . 10
65anbi2i 450 . . . . . . . . 9
7 an4 558 . . . . . . . . 9
8 ancom 264 . . . . . . . . . 10
98anbi1i 451 . . . . . . . . 9
106, 7, 93bitri 205 . . . . . . . 8
1110imbi1i 237 . . . . . . 7
12 impexp 261 . . . . . . 7
13 impexp 261 . . . . . . 7
1411, 12, 133bitri 205 . . . . . 6
1514albii 1429 . . . . 5
16 df-ral 2396 . . . . 5
17 r19.21v 2484 . . . . 5
1815, 16, 173bitr2i 207 . . . 4
1918albii 1429 . . 3
20 nfv 1491 . . . . 5
21 rmo2.1 . . . . 5
2220, 21nfan 1527 . . . 4
2322mo3 2029 . . 3
24 df-ral 2396 . . 3
2519, 23, 243bitr4i 211 . 2
261, 25bitri 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  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-ral 2396  df-rmo 2399 This theorem is referenced by:  disjiun  3892
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