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Theorem rabxfr 4202
 Description: Class builder membership after substituting an expression (containing ) for in the class expression . (Contributed by NM, 10-Jun-2005.)
Hypotheses
Ref Expression
rabxfr.1
rabxfr.2
rabxfr.3
rabxfr.4
rabxfr.5
Assertion
Ref Expression
rabxfr
Distinct variable groups:   ,   ,,   ,   ,
Allowed substitution hints:   ()   ()   ()   (,)   (,)

Proof of Theorem rabxfr
StepHypRef Expression
1 tru 1247 . 2
2 rabxfr.1 . . 3
3 rabxfr.2 . . 3
4 rabxfr.3 . . . 4
54adantl 262 . . 3
6 rabxfr.4 . . 3
7 rabxfr.5 . . 3
82, 3, 5, 6, 7rabxfrd 4201 . 2
91, 8mpan 400 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wtru 1244   wcel 1393  wnfc 2165  crab 2310 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rab 2315  df-v 2559 This theorem is referenced by: (None)
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