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Theorem rmoeq1f 3031
 Description: Equality theorem for restricted uniqueness 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 2602 . . 3
4 eleq2 2502 . . . 4
54anbi1d 709 . . 3
63, 5mobid 2287 . 2
7 df-rmo 2790 . 2
8 df-rmo 2790 . 2
96, 7, 83bitr4g 291 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wcel 1870  wmo 2267  wnfc 2577  wrmo 2785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-eu 2270  df-mo 2271  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rmo 2790 This theorem is referenced by:  rmoeq1  3035
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