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Theorem gencl 3139
 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 219 . . . 4
54impcom 430 . . 3
65exlimiv 1723 . 2
71, 6sylbi 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1395  wex 1613 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614 This theorem is referenced by:  2gencl  3140  3gencl  3141  indpi  9302  axrrecex  9557
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