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Theorem gencl 2718
 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 153 . . . 4
54impcom 124 . . 3
65exlimiv 1577 . 2
71, 6sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-gen 1425  ax-ie2 1470  ax-17 1506 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  2gencl  2719  3gencl  2720  axprecex  7688  axpre-ltirr  7690
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