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Theorem elsb3 1894
 Description: Substitution applied to an atomic membership wff. (Contributed by NM, 7-Nov-2006.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
elsb3
Distinct variable group:   ,

Proof of Theorem elsb3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-17 1460 . . . . 5
2 elequ1 1641 . . . . 5
31, 2sbieh 1714 . . . 4
43sbbii 1689 . . 3
5 ax-17 1460 . . . 4
65sbco2h 1880 . . 3
74, 6bitr3i 184 . 2
8 equsb1 1709 . . . 4
9 elequ1 1641 . . . . 5
109sbimi 1688 . . . 4
118, 10ax-mp 7 . . 3
12 sbbi 1875 . . 3
1311, 12mpbi 143 . 2
14 ax-17 1460 . . 3
1514sbh 1700 . 2
167, 13, 153bitri 204 1
 Colors of variables: wff set class Syntax hints:   wb 103  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687 This theorem is referenced by:  cvjust  2077
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