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Theorem rmo4 3029
 Description: Restricted "at most one" using implicit substitution. (Contributed by NM, 24-Oct-2006.) (Revised by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmo4.1
Assertion
Ref Expression
rmo4
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rmo4
StepHypRef Expression
1 df-rmo 2622 . 2
2 an4 797 . . . . . . . . 9
3 ancom 437 . . . . . . . . . 10
43anbi1i 676 . . . . . . . . 9
52, 4bitri 240 . . . . . . . 8
65imbi1i 315 . . . . . . 7
7 impexp 433 . . . . . . 7
8 impexp 433 . . . . . . 7
96, 7, 83bitri 262 . . . . . 6
109albii 1566 . . . . 5
11 df-ral 2619 . . . . 5
12 r19.21v 2701 . . . . 5
1310, 11, 123bitr2i 264 . . . 4
1413albii 1566 . . 3
15 eleq1 2413 . . . . 5
16 rmo4.1 . . . . 5
1715, 16anbi12d 691 . . . 4
1817mo4 2237 . . 3
19 df-ral 2619 . . 3
2014, 18, 193bitr4i 268 . 2
211, 20bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wcel 1710  wmo 2205  wral 2614  wrmo 2617 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-ral 2619  df-rmo 2622 This theorem is referenced by:  reu4  3030
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