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Theorem rmob 3241
 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 2705 . 2
2 simprl 733 . . . 4
3 eleq1 2495 . . . 4
42, 3syl5ibcom 212 . . 3
5 simpl 444 . . . 4
65a1i 11 . . 3
7 simplrl 737 . . . . 5
8 simpr 448 . . . . 5
9 simpll 731 . . . . 5
10 simplrr 738 . . . . 5
11 eleq1 2495 . . . . . . 7
12 rmoi.b . . . . . . 7
1311, 12anbi12d 692 . . . . . 6
14 eleq1 2495 . . . . . . 7
15 rmoi.c . . . . . . 7
1614, 15anbi12d 692 . . . . . 6
1713, 16mob 3108 . . . . 5
187, 8, 9, 7, 10, 17syl212anc 1194 . . . 4
1918ex 424 . . 3
204, 6, 19pm5.21ndd 344 . 2
211, 20sylanb 459 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wmo 2281  wrmo 2700 This theorem is referenced by:  rmoi  3242 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rmo 2705  df-v 2950
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