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Theorem gencl 2976
 Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.)
Hypotheses
Ref Expression
gencl.1
gencl.2
gencl.3
Assertion
Ref Expression
gencl
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem gencl
StepHypRef Expression
1 gencl.1 . 2
2 gencl.3 . . . . 5
3 gencl.2 . . . . 5
42, 3syl5ib 211 . . . 4
54impcom 420 . . 3
65exlimiv 1644 . 2
71, 6sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652 This theorem is referenced by:  2gencl  2977  3gencl  2978  indpi  8776  axrrecex  9030 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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