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Theorem rmo3 2877
 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 2331 . 2
2 sban 1845 . . . . . . . . . . 11
3 clelsb3 2158 . . . . . . . . . . . 12
43anbi1i 439 . . . . . . . . . . 11
52, 4bitri 177 . . . . . . . . . 10
65anbi2i 438 . . . . . . . . 9
7 an4 528 . . . . . . . . 9
8 ancom 257 . . . . . . . . . 10
98anbi1i 439 . . . . . . . . 9
106, 7, 93bitri 199 . . . . . . . 8
1110imbi1i 231 . . . . . . 7
12 impexp 254 . . . . . . 7
13 impexp 254 . . . . . . 7
1411, 12, 133bitri 199 . . . . . 6
1514albii 1375 . . . . 5
16 df-ral 2328 . . . . 5
17 r19.21v 2413 . . . . 5
1815, 16, 173bitr2i 201 . . . 4
1918albii 1375 . . 3
20 nfv 1437 . . . . 5
21 rmo2.1 . . . . 5
2220, 21nfan 1473 . . . 4
2322mo3 1970 . . 3
24 df-ral 2328 . . 3
2519, 23, 243bitr4i 205 . 2
261, 25bitri 177 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wal 1257  wnf 1365   wcel 1409  wsb 1661  wmo 1917  wral 2323  wrmo 2326 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-cleq 2049  df-clel 2052  df-ral 2328  df-rmo 2331 This theorem is referenced by: (None)
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