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Theorem 3gencl 2605
 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:   ,,   ,,   ,   ,,   ,,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,)   (,,)   (,,)   (,,)   ()   ()   ()   (,)   (,,)

Proof of Theorem 3gencl
StepHypRef Expression
1 3gencl.3 . . . . 5
2 df-rex 2329 . . . . 5
31, 2bitri 177 . . . 4
4 3gencl.6 . . . . 5
54imbi2d 223 . . . 4
6 3gencl.1 . . . . . 6
7 3gencl.2 . . . . . 6
8 3gencl.4 . . . . . . 7
98imbi2d 223 . . . . . 6
10 3gencl.5 . . . . . . 7
1110imbi2d 223 . . . . . 6
12 3gencl.7 . . . . . . 7
13123expia 1117 . . . . . 6
146, 7, 9, 11, 132gencl 2604 . . . . 5
1514com12 30 . . . 4
163, 5, 15gencl 2603 . . 3
1716com12 30 . 2
18173impia 1112 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   w3a 896   wceq 1259  wex 1397   wcel 1409  wrex 2324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354  ax-ie2 1399  ax-17 1435 This theorem depends on definitions:  df-bi 114  df-3an 898  df-rex 2329 This theorem is referenced by:  axpre-ltwlin  7015  axpre-lttrn  7016  axpre-ltadd  7018  axpre-mulext  7020
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