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Theorem rmoi 2972
 Description: Consequence of "at most one", using implicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
rmoi.b
rmoi.c
Assertion
Ref Expression
rmoi
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rmoi
StepHypRef Expression
1 rmoi.b . . 3
2 rmoi.c . . 3
31, 2rmob 2971 . 2
43biimp3ar 1307 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 945   wceq 1314   wcel 1463  wrmo 2394 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rmo 2399  df-v 2660 This theorem is referenced by: (None)
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