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Theorem rmo3 2843
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  F/
Assertion
Ref Expression
rmo3
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem rmo3
StepHypRef Expression
1 df-rmo 2308 . 2
2 sban 1826 . . . . . . . . . . 11
3 clelsb3 2139 . . . . . . . . . . . 12
43anbi1i 431 . . . . . . . . . . 11
52, 4bitri 173 . . . . . . . . . 10
65anbi2i 430 . . . . . . . . 9
7 an4 520 . . . . . . . . 9
8 ancom 253 . . . . . . . . . 10
98anbi1i 431 . . . . . . . . 9
106, 7, 93bitri 195 . . . . . . . 8
1110imbi1i 227 . . . . . . 7
12 impexp 250 . . . . . . 7
13 impexp 250 . . . . . . 7
1411, 12, 133bitri 195 . . . . . 6
1514albii 1356 . . . . 5
16 df-ral 2305 . . . . 5
17 r19.21v 2390 . . . . 5
1815, 16, 173bitr2i 197 . . . 4
1918albii 1356 . . 3
20 nfv 1418 . . . . 5  F/
21 rmo2.1 . . . . 5  F/
2220, 21nfan 1454 . . . 4  F/
2322mo3 1951 . . 3
24 df-ral 2305 . . 3
2519, 23, 243bitr4i 201 . 2
261, 25bitri 173 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   F/wnf 1346   wcel 1390  wsb 1642  wmo 1898  wral 2300  wrmo 2303
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-cleq 2030  df-clel 2033  df-ral 2305  df-rmo 2308
This theorem is referenced by: (None)
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