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Theorem 2gencl 3109
 Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.)
Hypotheses
Ref Expression
2gencl.1
2gencl.2
2gencl.3
2gencl.4
2gencl.5
Assertion
Ref Expression
2gencl
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   (,)   (,)   ()   (,)   ()   ()

Proof of Theorem 2gencl
StepHypRef Expression
1 2gencl.2 . . . 4
2 df-rex 2779 . . . 4
31, 2bitri 252 . . 3
4 2gencl.4 . . . 4
54imbi2d 317 . . 3
6 2gencl.1 . . . . . 6
7 df-rex 2779 . . . . . 6
86, 7bitri 252 . . . . 5
9 2gencl.3 . . . . . 6
109imbi2d 317 . . . . 5
11 2gencl.5 . . . . . 6
1211ex 435 . . . . 5
138, 10, 12gencl 3108 . . . 4
1413com12 32 . . 3
153, 5, 14gencl 3108 . 2
1615impcom 431 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437  wex 1659   wcel 1867  wrex 2774 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-rex 2779 This theorem is referenced by:  3gencl  3110  axaddrcl  9565  axmulrcl  9567  axpre-lttri  9578  axpre-mulgt0  9581  uzin2  13375
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