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Theorem rmo4f 25849
 Description: Restricted "at most one" using implicit substitution. (Contributed by NM, 24-Oct-2006.) (Revised by Thierry Arnoux, 11-Oct-2016.) (Revised by Thierry Arnoux, 8-Mar-2017.) (Revised by Thierry Arnoux, 8-Oct-2017.)
Hypotheses
Ref Expression
rmo4f.1
rmo4f.2
rmo4f.3
rmo4f.4
Assertion
Ref Expression
rmo4f
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   (,)

Proof of Theorem rmo4f
StepHypRef Expression
1 rmo4f.1 . . 3
2 rmo4f.2 . . 3
3 nfv 1673 . . 3
41, 2, 3rmo3f 25847 . 2
5 rmo4f.3 . . . . . 6
6 rmo4f.4 . . . . . 6
75, 6sbie 2100 . . . . 5
87anbi2i 694 . . . 4
98imbi1i 325 . . 3
1092ralbii 2736 . 2
114, 10bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wnf 1589  wsb 1700  wnfc 2561  wral 2710  wrmo 2713 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2256  df-mo 2257  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2715  df-rmo 2718 This theorem is referenced by:  disjorf  25891  funcnv5mpt  25956
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