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Theorem rabxfr 4674
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:   ,   , ,   ,   ,

Proof of Theorem rabxfr
StepHypRef Expression
1 tru 1399 . 2
2 rabxfr.1 . . 3
3 rabxfr.2 . . 3
4 rabxfr.3 . . . 4
54adantl 466 . . 3
6 rabxfr.4 . . 3
7 rabxfr.5 . . 3
82, 3, 5, 6, 7rabxfrd 4673 . 2
91, 8mpan 670 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395   wtru 1396  e.wcel 1818  F/_wnfc 2605  {crab 2811
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111
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