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Theorem clelsb3f 2233
 Description: Substitution applied to an atomic wff (class version of elsb3 1901). (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (Revised by Thierry Arnoux, 13-Mar-2017.)
Hypothesis
Ref Expression
clelsb3f.1
Assertion
Ref Expression
clelsb3f

Proof of Theorem clelsb3f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 clelsb3f.1 . . . 4
21nfcri 2223 . . 3
32sbco2 1888 . 2
4 nfv 1467 . . . 4
5 eleq1w 2149 . . . 4
64, 5sbie 1722 . . 3
76sbbii 1696 . 2
8 nfv 1467 . . 3
9 eleq1w 2149 . . 3
108, 9sbie 1722 . 2
113, 7, 103bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wb 104   wcel 1439  wsb 1693  wnfc 2216 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-cleq 2082  df-clel 2085  df-nfc 2218 This theorem is referenced by:  rmo3f  2813
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