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Theorem rmob 3134
 Description: Consequence of "at most one", using implicit substitution. (Contributed by NM, 2-Jan-2015.) (Revised by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
rmoi.b
rmoi.c
Assertion
Ref Expression
rmob
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rmob
StepHypRef Expression
1 df-rmo 2622 . 2
2 simprl 732 . . . 4
3 eleq1 2413 . . . 4
42, 3syl5ibcom 211 . . 3
5 simpl 443 . . . 4
65a1i 10 . . 3
7 simplrl 736 . . . . 5
8 simpr 447 . . . . 5
9 simpll 730 . . . . 5
10 simplrr 737 . . . . 5
11 eleq1 2413 . . . . . . 7
12 rmoi.b . . . . . . 7
1311, 12anbi12d 691 . . . . . 6
14 eleq1 2413 . . . . . . 7
15 rmoi.c . . . . . . 7
1614, 15anbi12d 691 . . . . . 6
1713, 16mob 3018 . . . . 5
187, 8, 9, 7, 10, 17syl212anc 1192 . . . 4
1918ex 423 . . 3
204, 6, 19pm5.21ndd 343 . 2
211, 20sylanb 458 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  wmo 2205  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-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rmo 2622  df-v 2861 This theorem is referenced by:  rmoi  3135
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