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Theorem 2gencl 2987
 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 2713 . . . 4
31, 2bitri 242 . . 3
4 2gencl.4 . . . 4
54imbi2d 309 . . 3
6 2gencl.1 . . . . . 6
7 df-rex 2713 . . . . . 6
86, 7bitri 242 . . . . 5
9 2gencl.3 . . . . . 6
109imbi2d 309 . . . . 5
11 2gencl.5 . . . . . 6
1211ex 425 . . . . 5
138, 10, 12gencl 2986 . . . 4
1413com12 30 . . 3
153, 5, 14gencl 2986 . 2
1615impcom 421 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726  wrex 2708 This theorem is referenced by:  3gencl  2988  axaddrcl  9029  axmulrcl  9031  axpre-lttri  9042  axpre-mulgt0  9045  uzin2  12150 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-rex 2713
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