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Theorem 2gencl 2719
 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 2422 . . . 4
31, 2bitri 183 . . 3
4 2gencl.4 . . . 4
54imbi2d 229 . . 3
6 2gencl.1 . . . . . 6
7 df-rex 2422 . . . . . 6
86, 7bitri 183 . . . . 5
9 2gencl.3 . . . . . 6
109imbi2d 229 . . . . 5
11 2gencl.5 . . . . . 6
1211ex 114 . . . . 5
138, 10, 12gencl 2718 . . . 4
1413com12 30 . . 3
153, 5, 14gencl 2718 . 2
1615impcom 124 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wex 1468   wcel 1480  wrex 2417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1425  ax-ie2 1470  ax-17 1506 This theorem depends on definitions:  df-bi 116  df-rex 2422 This theorem is referenced by:  3gencl  2720  axaddrcl  7680  axmulrcl  7682  axpre-apti  7700  axpre-mulgt0  7702  uzin2  10766
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