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Theorem gencl 2816
 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 210 . . . 4
54impcom 419 . . 3
65exlimiv 1666 . 2
71, 6sylbi 187 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1528   wceq 1623 This theorem is referenced by:  2gencl  2817  3gencl  2818  indpi  8531  axrrecex  8785 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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