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Theorem rmoeq1f 2905
 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 2581 . . 3
4 eleq2 2499 . . . 4
54anbi1d 687 . . 3
63, 5mobid 2317 . 2
7 df-rmo 2715 . 2
8 df-rmo 2715 . 2
96, 7, 83bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wmo 2284  wnfc 2561  wrmo 2710 This theorem is referenced by:  rmoeq1  2909 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rmo 2715
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