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Theorem csbiedf 3280
 Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbiedf.1
csbiedf.2
csbiedf.3
csbiedf.4
Assertion
Ref Expression
csbiedf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem csbiedf
StepHypRef Expression
1 csbiedf.1 . . 3
2 csbiedf.4 . . . 4
32ex 424 . . 3
41, 3alrimi 1781 . 2
5 csbiedf.3 . . 3
6 csbiedf.2 . . 3
7 csbiebt 3279 . . 3
85, 6, 7syl2anc 643 . 2
94, 8mpbid 202 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553   wceq 1652   wcel 1725  wnfc 2558  csb 3243 This theorem is referenced by:  csbied  3285  csbie2t  3287  natpropd  14165  fucpropd  14166  sumsnd  27664 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-3an 938  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  df-sbc 3154  df-csb 3244
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