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Theorem ceqsexg 3059
 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:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ceqsexg
StepHypRef Expression
1 nfcv 2571 . 2
2 nfe1 1747 . . 3
3 ceqsexg.1 . . 3
42, 3nfbi 1856 . 2
5 ceqex 3058 . . 3
6 ceqsexg.2 . . 3
75, 6bibi12d 313 . 2
8 biid 228 . 2
91, 4, 7, 8vtoclgf 3002 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652   wcel 1725 This theorem is referenced by:  ceqsexgv  3060 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950
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