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Theorem eqrdav 2437
 Description: Deduce equality of classes from an equivalence of membership that depends on the membership variable. (Contributed by NM, 7-Nov-2008.)
Hypotheses
Ref Expression
eqrdav.1
eqrdav.2
eqrdav.3
Assertion
Ref Expression
eqrdav
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eqrdav
StepHypRef Expression
1 eqrdav.1 . . . 4
2 eqrdav.3 . . . . . 6
32biimpd 200 . . . . 5
43impancom 429 . . . 4
51, 4mpd 15 . . 3
6 eqrdav.2 . . . 4
72exbiri 607 . . . . . 6
87com23 75 . . . . 5
98imp 420 . . . 4
106, 9mpd 15 . . 3
115, 10impbida 807 . 2
1211eqrdv 2436 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726 This theorem is referenced by:  boxcutc  7107  supminf  10565  fmucndlem  18323  ballotlemsima  24775  f1omvdconj  27368 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-cleq 2431
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