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Theorem 3gencl 3141
 Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.)
Hypotheses
Ref Expression
3gencl.1
3gencl.2
3gencl.3
3gencl.4
3gencl.5
3gencl.6
3gencl.7
Assertion
Ref Expression
3gencl
Distinct variable groups:   ,,   ,,   ,   ,,   ,S,   ,   ,   ,

Proof of Theorem 3gencl
StepHypRef Expression
1 3gencl.3 . . . . 5
2 df-rex 2813 . . . . 5
31, 2bitri 249 . . . 4
4 3gencl.6 . . . . 5
54imbi2d 316 . . . 4
6 3gencl.1 . . . . . 6
7 3gencl.2 . . . . . 6
8 3gencl.4 . . . . . . 7
98imbi2d 316 . . . . . 6
10 3gencl.5 . . . . . . 7
1110imbi2d 316 . . . . . 6
12 3gencl.7 . . . . . . 7
13123expia 1198 . . . . . 6
146, 7, 9, 11, 132gencl 3140 . . . . 5
1514com12 31 . . . 4
163, 5, 15gencl 3139 . . 3
1716com12 31 . 2
18173impia 1193 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818  E.wrex 2808 This theorem is referenced by:  axpre-lttrn  9564  axpre-ltadd  9565 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-rex 2813
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