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Theorem ceqsexg 3231
Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 11-Oct-2004.)
Hypotheses
Ref Expression
ceqsexg.1
ceqsexg.2
Assertion
Ref Expression
ceqsexg
Distinct variable group:   ,

Proof of Theorem ceqsexg
StepHypRef Expression
1 nfe1 1840 . . 3
2 ceqsexg.1 . . 3
31, 2nfbi 1934 . 2
4 ceqex 3230 . . 3
5 ceqsexg.2 . . 3
64, 5bibi12d 321 . 2
7 biid 236 . 2
83, 6, 7vtoclg1f 3166 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818
This theorem is referenced by:  ceqsexgv  3232
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-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-v 3111
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