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Theorem rmo3 3429
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:   , ,

Proof of Theorem rmo3
StepHypRef Expression
1 df-rmo 2815 . 2
2 sban 2140 . . . . . . . . . . 11
3 clelsb3 2578 . . . . . . . . . . . 12
43anbi1i 695 . . . . . . . . . . 11
52, 4bitri 249 . . . . . . . . . 10
65anbi2i 694 . . . . . . . . 9
7 an4 824 . . . . . . . . 9
8 ancom 450 . . . . . . . . . 10
98anbi1i 695 . . . . . . . . 9
106, 7, 93bitri 271 . . . . . . . 8
1110imbi1i 325 . . . . . . 7
12 impexp 446 . . . . . . 7
13 impexp 446 . . . . . . 7
1411, 12, 133bitri 271 . . . . . 6
1514albii 1640 . . . . 5
16 df-ral 2812 . . . . 5
17 r19.21v 2862 . . . . 5
1815, 16, 173bitr2i 273 . . . 4
1918albii 1640 . . 3
20 nfv 1707 . . . . 5
21 rmo2.1 . . . . 5
2220, 21nfan 1928 . . . 4
2322mo3 2323 . . 3
24 df-ral 2812 . . 3
2519, 23, 243bitr4i 277 . 2
261, 25bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616  [wsb 1739  e.wcel 1818  E*wmo 2283  A.wral 2807  E*wrmo 2810
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-ral 2812  df-rmo 2815
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