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Theorem rmoeq1f 2623
 Description: Equality theorem for restricted at-most-one quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypotheses
Ref Expression
raleq1f.1
raleq1f.2
Assertion
Ref Expression
rmoeq1f

Proof of Theorem rmoeq1f
StepHypRef Expression
1 raleq1f.1 . . . 4
2 raleq1f.2 . . . 4
31, 2nfeq 2287 . . 3
4 eleq2 2201 . . . 4
54anbi1d 460 . . 3
63, 5mobid 2032 . 2
7 df-rmo 2422 . 2
8 df-rmo 2422 . 2
96, 7, 83bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331   wcel 1480  wmo 1998  wnfc 2266  wrmo 2417 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rmo 2422 This theorem is referenced by:  rmoeq1  2627
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