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Theorem 2gencl 2817
 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 2549 . . . 4
31, 2bitri 240 . . 3
4 2gencl.4 . . . 4
54imbi2d 307 . . 3
6 2gencl.1 . . . . . 6
7 df-rex 2549 . . . . . 6
86, 7bitri 240 . . . . 5
9 2gencl.3 . . . . . 6
109imbi2d 307 . . . . 5
11 2gencl.5 . . . . . 6
1211ex 423 . . . . 5
138, 10, 12gencl 2816 . . . 4
1413com12 27 . . 3
153, 5, 14gencl 2816 . 2
1615impcom 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1528   wceq 1623   wcel 1684  wrex 2544 This theorem is referenced by:  3gencl  2818  axaddrcl  8774  axmulrcl  8776  axpre-lttri  8787  axpre-mulgt0  8790  uzin2  11828 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-rex 2549
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