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Theorem elsb3 2132
 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 1503 . . . . 5
2 elequ1 2129 . . . . 5
31, 2sbieh 1767 . . . 4
43sbbii 1742 . . 3
5 ax-17 1503 . . . 4
65sbco2h 1941 . . 3
74, 6bitr3i 185 . 2
8 equsb1 1762 . . . 4
9 elequ1 2129 . . . . 5
109sbimi 1741 . . . 4
118, 10ax-mp 5 . . 3
12 sbbi 1936 . . 3
1311, 12mpbi 144 . 2
14 ax-17 1503 . . 3
1514sbh 1753 . 2
167, 13, 153bitri 205 1
 Colors of variables: wff set class Syntax hints:   wb 104  wsb 1739 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-13 2127 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1740 This theorem is referenced by:  cvjust  2149
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